It sounds like your Dometic unit is not getting power despite the breaker being on. Unless the Dometic unit has an internal fuse to check, I would get out a volt/ohm meter and check to see:
1. Is there power coming out of the breaker that goes to the ac unit?
2. Is there power at the terminals of the ac unit? (You can sometimes remove a ceiling cover to access the contacts on the on off switch.

Lastly is your RV hooked up to full power with two 110 volts on both legs beside the neutral and ground wire? If you are only feeding your RV with a standard 110 volt extension cord and using an adapter, that can mean half the circuits in your RV are energized while the other half 110 volt leg is not. You must energize the second leg by using a full 30 amp or 50 amp dual power cord.

RV's are funny. They require two 110 volt legs with a neutral and a ground. The two 110 volt legs are both of the same phase. There is no 220 volts between the two hot legs as they are in phase. A volt meter between the when hot would read zero volts, while each hot leg to neutral would read 110 volts.

Hope this helps.