The problem is the motors have no provision for starting, that is supplied
by the motor drive circuit that gradually increases applied voltage and
frequency as the motor picks up speed.
If the windings are not shorted to the housing, the motor is most likely
good. (Can't test the compressor as a whole so simply.)
The drive circuits are VERY complex, probably using IGBTs and a logic
circuit to drive them, which likely has a microprocessor in it.
I'm not sure we can really tell you how to test the drive circuit on such a
forum as this. And, be aware there are dangerous voltages in such circuits.
Jon