My guess is that the A/C uses relays for controlling high current loads, like the fan, compressor and pump.
It may be that the A/C has a multiple pole relay, with separate feeds for each load. It is more likely that all loads are switched with the same contact, so if the pump is working in that configuration that points to the fan motor having a problem.
Easiest way is to dig in. There is probably a wiring diagram on the inside cover for the electronics.
