Hi Jim,
Sorry you're having a problem with the A/C. If your unit just makes a humming sound, it seems like maybe the blower is not running.
To investigate, you might try switching the thermostat to FAN mode and set it on HIGH. The A/C fan should come on and blow on high (without any cooling).
If it doesn't, you might want to cut off the circuit breaker and remove the cover on top of the A/C unit to see if perhaps there's something obstructing the blower. When you open it, watch out for wasps or other insects that might cause you to jump back and fall. With power off, you can look for something that might be interfering with the blower operation.
Btw, I think you'll find that this same Dometic A/C unit is used by most if not all RV manufacturers. You could have had the same problem with a coach that cost $50,000 more than you paid.