Disconnect the fan and see if the compressor will run. If the fan is bad and drawing too much power, the compressor controller will shut down as a self-protection.
If you can access the compressor electronic module, you can hook up an LED light across the D and + terminals and get error (flash) codes. Fan being faulty (drawing more than one amp) would be two flashes. There are other codes for other problems.
(You can just experiment with the fan but the light can be handy for future use.)