Let me be sure I understand:
1. Fan works but not Compressor (air moving but not chilled).
2. A/C has manual controls on it (no wall thermostat).
If that's the case, my thoughts are:
1. Switch defective or in wrong position
2. Problem with Defrost Sensor (if it has one - Our Coleman with controls on unit does NOT)
3. Bad Compressor or Bad Thermal Safety on Compressor (unlikely)
4. Bad Run Capacitor on Compressor (a prime suspect)
Are you comfortable getting onto the roof of the RV and digging into an electrical device?
Do you have a Clamp-On Ammeter?
A Digital (or old Analog) Volt/Ohm Meter?
If you have a meter, can it measure Capacitance (MicroFarads (maybe labeled uF")?