Uh, oh. I assumed from your posts the fan was operating normally and the compressor wasn't. If the fan is still having problems this puts an entirely different light on the problem. I'd concentrate on the fan first. It's really simple, it's a permanent split capacitor motor.

Single Phase Motor Starting

The fan could not start without the capacitor, there would be only one winding energized. The fact that it will start but then stops, and then restarts sounds like either a capacitor problem or a connection problem. If you can get the fan to work, whatever you find will probably apply to the compressor also. I'd recommend disconnecting the compressor and working with the fan alone until you find out what's going on. Don't what to shell out the compressor with your troubleshooting efforts..