After repeatedly trying to start your small engine without success, you have most likely flooded the engine. When you keep priming and trying to start a small engine, the carburetor will become flooded with gas and rather than injecting a mist of gas into the piston chamber, the carburetor will drip gas into it and that won't properly mix with the air so the engine won't fire properly.
Unscrew the air filter cover from the small engine with the flathead screwdriver.
Pull the cover off and pull out the air filter.
Insert the screwdriver into the air intake valve of the engine. By doing this you will force the butterfly valve open and allow for maximum air intake and therefore enough air to counter all the gas in the piston chamber.
Turn the key or pull start the engine until it starts. Allow it to run for two to three minutes in order to burn all the excess gasoline.
Shut off the mower. Replace the air filter and air filter cover.