It could be a thermostat communication problem. More than likely the thermostat operates on 12v DC, you need to verify somehow that your getting 12v at the thermostat.
Someone needs to verify that the AC unit is actually receiving the call from the thermostat to operate, which would tell the unit via a relay or contactor to start the compressor. I'm not sure on an RV but on household thermostats, Usually the yellow wire is call for cool communication wire, the red thermostat wire is normally the power wire for the thermostat. I'm not sure if the RV industry uses the same house type thermostat wire.
Due to the fact your heat is not working either you could have a bad thermostat or it could be as simple as a bad wire connection or broken wire.
There are quite a few things that could cause this issue. It could be a blown fuse, tripped breaker, loose wire terminal connection.
Verify the simple stuff first, are you sure your getting 120v electric power? Are you sure there us not an open neutral? Then check breakers, fuses, and wire terminals.
I know more about residential and commercial systems than I do RV's so just trying to help.