Recently my bedroom air quit working. After a bit of troubleshooting, I determined the switch that was mounted on the AC unit was bad, not delivering voltage to the compressor. A new switch was hard to find, but I finally did at $27 and it fixed the problem.
My main troubleshooting steps were:
1) Inspect the AC unit on the roof, to see if I could find leaking freon. Turns out this was a wasted step because low freon in this particular AC unit does NOT cause the compressor to NOT turn on.
2) Turn off the AC main breaker and the inverter to remove all power! Take the AC cover off in the bedroom. Remove the cover to the switch. Ohm out the switch. It actually ohm'd good. Re-apply power and trace the voltage signal (I'm an electrical engineer, don't do this if you don't understand 120V circuits.) The voltage was not appearing on the compressor terminal, hence the switch was not passing it, even though it ohm'd OK.
3) Build a bypass cable and jumper the AC around the switch. Wahlah! The compressor came on a got cold. Hence the switch was bad.
This is a bedroom Dometic that has the thermostat and switch actually mounted on the AC unit. If your AC unit has a wall thermostat, this answer doesn't apply.
By the way, I took the old switch apart for fun, and found the problem and fixed it. SO now I have a spare switch!