As Desire Brazell watched her 19-year-old son walk out the door on Valentine's Day 2005, she couldnât imagine the heartbreak ahead.  Her child Rashawn was beheaded and dismembered in a gruesome killing that remains a total whodunit: An ice-cold case with seemingly no chance of ever warming up. But the mom, despite the long stretch of justice denied, refuses to surrender.  "I know someone out there knows something and they're not talking," Desire Brazell told the Daily News. "It amazes me you can walk around every day knowing you know what you know and you're not saying anything."  She has good reason to feel that way.  Rashawn left their Bushwick home on the morning of Feb. 14, 2005, headed to the nearby Gates Avenue subway station.  Three days later, a bag containing some of his body parts was found between the Franklin and Nostrand Avenue stations on the A line. More pieces of the dead teen were discovered at a recycling center where subway garbage is taken.  His head is still missing.  That type of cold-blooded murder, his mother believes, had to have involved more than one person.  Perhaps. But right now the NYPD Cold Case Squad, assigned the case about six months ago, faces more questions than answers.  It's not clear where Brazell was killed, for instance, nor was a motive ever established.  Brazell's mother, a social services caseworker, thinks clues can be gleaned from a mysterious outgoing voicemail message her son recorded on his cellphone at the start of 2005.  The message referred to him making changes and warned those unable to reach him to realize they werenât part of his new plan.  "Anything serious going on?" his mother asked. "He said, 'No, everything is fine.' Next month he was gone."  Lt. David Nilsen, who heads Cold Case, said there was no evidence to suggest Brazell's bisexuality was the motive for his killing. But even that's hardly etched in stone.  "I won't say for sure it wasn't a hate crime," Nilsen said. "I don't think that's fair to the deceased until we know everything and we have the guy and we have the exact motivation (as to) why you would commit such a heinous act."  The Brazell homicide is one among thousands of unsolved New York murders going back decades, including more than 1,700 since 2006.  Nilsen supervises 20 detectives and three sergeants for a unit that at any given time is investigating about 120 murders.  Another 100 or so killings sit on the NYPD inactive list, though regular investigative steps â like re-submitting DNA evidence into an ever-expanding database â are taken.  Each homicide brings its own challenges. And the following cases offer a small sampling of the daunting task ahead as new cops pursue justice in these old murders:  The languishing investigation into the assassination of Run DMC rap legend Jam Master Jay doesnât lack for suspects.  In fact, itâs a murder with too many.  But 14 years later, witnesses refuse to give cops any identifying details for the gunman who shot the hip-hop star in the back of the head at a Jamaica, Queens, recording studio.  âExactly what happened, definitively? Weâre still trying to work out a few things,â Nilsen said.  Several people were in the studio where Jam Master Jay â whose real name was Jason Mizell â was shot and killed on Oct. 30, 2002.  Over the years, investigators have identified at least three possible suspects.  One had threatened to visit the ground-breaking DJ to settle a decade-old drug debt. Another appeared inside the studio waving a gun around, possibly to distract attention away from the real killer.  Yet no one who witnessed the turntable masterâs murder will speak to detectives.  âWe believe we have the structure of what happened ... how it happened,â Nilsen said. âI canât really divulge what itâs about at this stage.â  Mizellâs murder is one of the cityâs most notable unsolved cases, rivaling the â90s murders of hip-hop stars Biggie Smalls in Los Angeles and Tupac Shakur in Las Vegas.  The chances of an arrest in Mizellâs murder dwindle with each passing year. But the hip-hop starâs family remains hopeful.  âHe never showed nothing but love to us,â said Mizellâs 81-year-old mother Connie Perry, speaking from her home in North Carolina. âWhoever killed him, God ainât finished with âem. God might have taken them already.â  Mizellâs sister Bernita Jones, 58, said investigators have stopped giving the family case updates.  âTheyâre not telling us nothing,â Jones said. âIt puzzles me that they have no idea what happened.â  Jones said she spoke to her brother the day before his death, and had a feeling of impending horror.  âI felt that something was off. It was just a vibe,â she said. âI told him to watch his back and he just said, âYeah, I got it.â  âI donât know if he knew what was going on or not,â Jones said. âHe wasnât telling us. He never got his family involved.â  At 44 years and counting, the 1972 strangling of retired grocer David Kickenson is the oldest and coldest slaying under the squadâs investigation.  Detectives actually believe they have a pretty good idea who did the killing: A 60-something career burglar who choked the surprised 88-year-old victim dead with a phone cord in his Williamsburg apartment.  But prosecutors asked police to build a stronger case against the suspect before signing off on an arrest.  Kickenson's now 101-year-old son, Harry Kickenson, said his father spent his retirement years hanging out at a local Democratic club and playing pinochle. He remembers him as "very soft-spoken" and never angry.  "I can't imagine him having any enemies," the son said.  The night of the murder, Harry Kickenson received a call at his Long Island home from one of his father's neighbors. He recounted racing to his father's Stagg Walk apartment, where the slain senior citizen was "in the bathtub with a gag in his mouth."  The victim was also been stabbed and the apartment ransacked, though Cold Case Squad head Nilsen said cops were unable to determine what was stolen because the victims lived alone.  âThey couldn't have stolen much because he never had much money,â said the son, now living in Delray Beach, Fla. âHe wasn't wealthy.â  Harry Kickenson tries to take some comfort in knowing police might be closing in on the killer, but said his family is done waiting for answers.  âThey don't know where to begin,â he said. "And I tried to rationalize that there's very little I could do about it and try to go on living as well as I can.â  The 12-year-old murder of a Manhattan jogger is now a few steps closer to an arrest.  Police have âflaggedâ a person of interest in the killing of Sarah Fox, 21, who was found dead in a Manhattan park about a week after her 2004 disappearance, officials said.  The Juilliard studentâs death is eerily similar to the killing of Karina Vetrano, a 30-year-old jogger who was sexually assaulted and strangled as she went out for a run in a Queens park on Aug. 2, 2016.  Fox went jogging in Inwood Hill Park on May 18, 2004, and never returned to her nearby apartment. Her nude body was found about a week later in a remote area of the upper Manhattan park. It was badly decomposed and surrounded by petals and branches from a tulip tree.  Police said at the time that the arrangement of the yellow petals appeared to be some sort of ritual or tribute.  A botanist confirmed for detectives that the petals came from elsewhere in the park, suggesting the killer was someone with an intimate knowledge of the landscape.  Investigators originally had two potential suspects for the strangulation, but one has since provided detectives with an alibi.  The second man has moved out of the country with his family.  âWe have him flagged,â Nilsen said.  Neither suspect is Dimitry Sheinman, an artist and self-proclaimed clairvoyant who then-Manhattan District Attorney Robert Morgenthau declared was the âNo. 1 suspectâ shortly after the killing.  Sheinman was known for wandering the park with his unleashed dog, a Rhodesian ridgeback, sparking confrontations with other parkgoers.  But Sheinman was never charged, though he did re-emerge in headlines last year when he returned to New York from South Africa.  The married father of two proclaimed that the name of the killer came to him in a vision. Cops said it turned out Sheinman was seeing things.  âHe gave in detail certain facts,â Nilsen said. âMy question is how many of those are credible facts and how many of those are not credible facts. Some of them I will tell you are not credible facts.â  Cops hoped to get DNA from the two suspects, although none was found at the crime scene, Nilsen said.  "She was very badly decomposed,â the lieutenant said. âHer clothes were not found on her."  A motive for the killing remains wide open, Nilsen said.  âIt may not be a total stranger attack,â he said. âFor all we know itâs someone she had a past relationship with many, many years before. Some people never forget.â  Attempts to reach Foxâs family were unsuccessful.  After four decades, the grisly murder of Queens teenager Leslie Zaret remains unsolved â even though itâs apparent that she was killed by someone she knew, police said.  The popular 17-year-old John Bowne High School student was found naked and strangled inside the schoolyard of Public School 203 on Aug. 17, 1974.  Police said she was killed around midnight, but her body wasnât discovered for several hours.  âWe believe that she met someone, someone she probably knew,â Nilsen said. âAt some point they were walking through the schoolyard and hanging out and then something went terribly wrong, which caused her death.â  Police sources said that Zaret may have had sex with her killer or had been sexually abused before her death. Her clothes were found in a pile near her body in Bayside, officials said.  "We believe itâs either someone she knew for some period of time, or someone she met that night,â Nilsen said.  Over the decades several possible suspects have been interviewed and ruled out â leaving the investigation frozen in its tracks.  Even a renewed look into the murder led by NYPD Chief of Community Affairs Bureau Joanne Jaffe, who lived in Bayside and was 16 when the killing took place, has turned up nothing new.  Zaretâs grieving family is left with little hope that her killer will be found. Her sister Melissa Zaret, 63, now living in Manhattan, declined to comment when reached.  â(A new story on the killing) is not going to bring my sister back or close the case,â she said.  Henryk Siwiak, like many others, left his home in the Rockaways on Sept. 11, 2001, for Lower Manhattan and never returned.  Unlike the nearly 3,000 people murdered by terrorists at the World Trade Center, Siwiak's killer remains a mystery. The Polish immigrant was shot to death in Brooklyn on the day the World Trade Center came down.  His sister, who helped him settle into the American way of life when he arrived 11 months earlier, fears she and the slain man's family — a wife and two children left behind in Poland - will never get justice.  "I don't have any new information from police," said the sister, Lucyna Siwiak, 67. "Everyone in the family is upset because there is nothing."  Police are similarly frustrated. Each Sept. 11 for the last 15 years, detectives have handed out flyers at the crime scene, Decatur St. and Albany Ave. in Bedford-Stuyvesant, hoping to fill in the blanks left by the eight people who saw or heard some sort of confrontation between Siwiak and another man.  None recalled enough to identify the gunman.  Earlier that day, Siwiak was supposed to work a construction job in lower Manhattan, only to turn and head home in fear after the Twin Towers were leveled by terrorists, his sister recalled.  That night, Siwiak was set to start a second job as a night cleaner at a Pathmark on Albany Ave. But he got lost on the way, exiting the A train at a stop three miles from the store. While trying to find his way to the supermarket, Siwiak crossed paths with his killer.  About $50 was found in Siwiak's pockets when police arrived, and detectives remain unable to determine if the killing was a botched robbery or something more sinister.  Henryk Siwiak was last seen in Brooklyn on Sept. 11, 2001 (AP Photo/Bebeto Matthews)  His widow suspects her husband was mistaken for Middle Eastern â he had dark features and was wearing camouflage pants â but police said there is no evidence he was the victim of a hate crime.  As with many unsolved murders, the Siwiak file remains at the 79th Precinct, where detectives still work the case.  Lt. Anthony Caroselli said the most frustrating aspect of the investigation is his belief that someone out there â a witness, a confidant of the killer â knows who's responsible.  "I don't know why they wouldn't come forward," he said. "It's something that always bothered us."  Police ask anyone with information on any of the murders profiled in the Daily News to call Crime Stoppers at (800)-577-TIPS. All calls will be kept confidential.
Thousands of murders in New York City remain unsolved. Each homicide brings new challenges for the NYPD Cold Case Squad.