The first question you need to ask yourself is; Does everything that runs on 110-VAC operate when you're plugged into campsite power?
If it does, then you probably have a problem with the wiring to the generator and not just the output wires, but the control wires from your temperature control panel. And, you need to make sure your COACH battery is being charged properly. If not, your power control panel could be not operating properly. You got your 6-7 years on those original batteries, and I would suggest that you have new ones, just for peace of mind when you do use the RV.
So, change that battery first and then check things out again.