Yes, there is a way to reset the compressor on a window mounted air conditioner. Your window mounted air conditioner has a reset button mounted near the power cord that makes the entire air conditioner go back to factory defaults, including the air compressor. It also helps to unplug the air conditioner to clear the air conditioner's settings.
Turn the window mounted air conditioner off and unplug the cord from the wall. Let the window mounted air conditioner sit for ten minutes for all the power to go out from the capacitors in the unit.
Plug the power cord back into the wall outlet and turn the window mounted air conditioner back on. Turn the cooling dial down to the point where the compressor engages. If the compressor engages, then the unplugging was sufficient to reset the air compressor if not, advance to the next section.
Press the reset button located near the power cord for five seconds and then take your finger off the button. Wait ten minutes for the air conditioner to work through the reset operation. Turn the air conditioner cooling dial down for the air compressor to engage. If it does not, then the compressor may be faulty.
If the previous steps were not sufficient to fix the window mounted air conditioner, then the compressor needs to be serviced as resetting will not fix the problem.