bowtiedaddy,
I think the item you are talking about is the starting capacitor. They shouldn't be hard to size for the motor and starting load. I will bet your problem is with the centrifugal switch located inside the motor.
It has a set of contacts that switch the start capacitor out of the circuit after the motor gets up to speed. When the motor shuts off, the contacts are suppose to come together and put the capacitor back into the circuit for the next start.
Either malfunction will not allow the motor to start. The air compressor has to unload after it stops too, which gives it a fighting chance when it starts back up...it can't start with cylinders loaded full of compressed air.
The new capacitor should have been the same physical size as the old one. They have values printed on their case...voltage and capacity in micro-farads...try to get one the same size and see if that solves the problem. If it isn't the capacitor, it's the centrifugal switch. Good luck.
EDIT. There is another possibility..the pressure switch isn't closing properly and telling the motor to start..so I guess there are three options, bad start capacitor (too small), bum contacts or sticking centrifugal switch, OR defective pressure switch.
Stuart