There should be a diagram ON your A/C. At rooftop, remove plastic shroud, look on the metal ducting that covers the front part of the A/C. This is the Evaporator "indoor coil" area and it's a good idea to remove that and clean that coil. The diagram on ours is on the side of the unit, toward the left front.
It must be the FAN that isn't working since you mention you can spin it, and no way can you spin the sealed Compressor. The Start Capacitor is for the Compressor ONLY. Fan has, and needs it to start, a Run Capacitor around 5-7mfd. It may be a separate "can" or part of a two-chamber capacitor shared withe Compressor. Compressor side capacitor 30-40mfd, to help you tell which is which.
Verify there's power to the Fan Motor. If there is, turn it ON and give it a fast spin. If it continues to run, even slowly, try a new Run Capacitor. Available Amazon and of course an appliance parts shop. I carry a spare Capacitor. We have one A/C and if it fails in Florida, it's Fix or Go Home.
Motor has a thermal "safety" inside, buried in the windings. If it's failed, the motor won't run even with power and a good capacitor. Windings themselves can go bad. Either case is Replace Motor. A new motor is just over $100 on Amazon. I replaced ours, still have the motor. Bad Bearings but it runs on both speeds. It's possible to make one good motor out of two or more bad ones.
All I've said, depends on Power to the Motor. On ours, we don't have a Wall Thermostat, just a Fan Knob and a Temp Knob on the inside part of our Mach 15. If you have a Wall Thermostat and probably some kind of Control Box on your A/C unit, troubleshooting gets a lot harder. You must make sure you have power to the motor!
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB