What does the run capacitor do on a compressor and how does it affect compressor starting?
compressor starting run capacitor
Since it is a running capacitor, it should have no bearing on the starting of the compressor - it's purpose is to "phase" the start winding after it is running to reduce the power factor and consumption rate. The compressor should start and run with that cap disconnected, or you have an issue with the relay (ptc) or the compressor itself.
Source: compressor question