Just remember that your air cond/heat and refrigerator has to have 12 volts to run the thermostats.
If no 12v or even low 12v, the fridge 'will' come on with shore power but when it hits the temp set and shuts off, it will NOT be able to turn back on without 12v running to it. Same with air cond/heat. Been there done that. :(
Did you shut off all the breakers to converter and turn them back on?
I found many times it will trip a breaker but not all the way. Visually at a glance you can't see it. And then check the volts on the converter. You could also just have a cooked battery.
