I replaced the cap (with one slightly smaller and with a bleeder resistor-scrounged) and started the motor with the belt off the compressor, it starts and runs fine. The switch it kicking in and out like it is supposed to, and the cap is not getting hot.

I am now starting to wonder is maybe the motor is fine but the compressor is toast.

I am wondering if I should tear into the compressor pump to inspect the cylinder wall for galling.

Thanks for all you advise guys and I am sorry for being hosed up about the single phase motors tobyaxis.

Jim