Originally Posted by eubank
Well, damn. It wasn't the capacitor.
I guess it's the motor, which doesn't look to be in much better condition than Tom's; thankfully, however, Tom also sourced the replacement:
Bay Breeze Air Conditioner
The problem could also be the power cord, especially if your using an extension cord.
Another possibility is the start relay. If the terminals are burned or badly corroded, it will not allow proper start up.
Also, at the top of the compressor, underneath the cover, there is a limit switch, that could also be bad.