Not sure what you mean with regard to "the wire on the right", but I assure you, none are broken. If you clarify that, I'll tell you exactly where it's connected in the pictures.
As for the USB cable, the "kink" is there on purpose. When designing something, you always make sure nothing ever physically pulls on the electrical connections. Routing the cable in that way makes it possible to pull on the cable, but it's locked in place by the "kink", almost liked being tied in a knot. Thus the part of the cable that is past the kink always has slack and therefore doesn't move. This is called "stress relief" for the wires.
So yes it is possible the repeated flexing, pulling or yanking on the cable, could cause an internal break in one or more of the wires inside the cable. I didn't see any evidence of that, namely a loose area that would be right where the cable enters the chassis. The cable is quite tough, and the wires inside of it pretty robust. In any case, this is how I tested it:
You can see the area of the circuit board where the USB cable attaches. It is a line of solder connections on the lower right side, at the 4:00 position. A box with labels shows this. All USB 1.0, 1.1 and 2.0 use four wires. These wires are red, black, green and white. You can see the labels: "Vcc" (Voltage, common collector). Red goes here. It's the +5 volts from the computer. "GND" (Ground). It's the ground reference for the +5 volt input. "D+" and "D-" (Data +, and Data -). Green and White go there; it's the high speed serial data that goes back to the computer's USB controller. The last connection on the bottom, would be for a "shield ground", which is a woven wire covering outside of the other wires. It's there to protect the data signal from outside sources of electrical noise, but mostly to suppress any electrical noise that the data might produce which might cause interference with other devices. If a cable has this, it's called a "shielded" cable. Most of the time that connection isn't used. So the wires go through circuit board "lands" which connect them to the rest of the circuitry on the board. The wires are connected from the underside of the board, go through the board, and are soldered at those solder bumps you see.
Anyway. Those bumps are basically the end of the cable wires. So, using a multimeter to measure continuity (passing a small current from one end of a wire to the other), you can tell if the wires are broken or not. You touch one of the 4 pins, then one of the 4 solder bumps. One of them should always have continuity. You test all 4 wires the same way; then you test each bump to all of the others, to make sure none of them have continuity with each other. If they did, that would mean that they're shorted together inside. Then you can touch the outside metal part of the USB plug, and check the continuity to the bottom shield connection on the board. If it's not there, it won't cause the circuit not to work, and probably just means it's an unshielded cable. You can look on the back side of the board to see if anything's connected to it, to verify that's the case.
Just basic electronics, really