When mine would start and then shut down it was because of low voltage.
The "fridge thermostat runs off of DC". So a plugged into AC power fridge 'will' come on but when it reaches it's set temp and shuts off the thermostat can not turn it back on because of low DC voltage.
I battled that problem with 3 different repair guys until the 4th one came into my RV and walked straight back to my converter to test it. Converter was shot and frying the batteries.
I.E low voltage to the thermostat in fridge and air conditioning. Allowing them both to come on but when they hit the temp set on the thermostat they would shut off and not be able to come back on.
Newer RV's may not have this problem. Because (i think)they have inverters factory installed in them. But most older RV's still need DC power to run the thermostats in fridge's and air conditioners.