Hi
Lights, fridge, and various other items in the trailer run on 12VDC. That comes off your batter. It normally gets recharged by your converter (from shore power) or your solar setup (if you have one).
The microwave, AC units, and entertainment system normally run off of the 120V shore power. Some 120V stuff *can* run off of the inverter. That's not a good idea if you have shore power.
First thing to check is to see if you actually have shore power. A simple/cheap outlet tester lives in the socket by the stove on my trailer. That makes it really easy to tell if shore power is there or not.
Assuming shore power is present, next thing to check is the converter. A good check is to put a multimeter on the battery and see if it is up > 13.5V with shore power connected. If it's not, either the battery is in big trouble or the converter is not workin properly. The converter can indeed blow out. It also can shut down if a breaker trips.
In any case, you should have some way to monitor battery voltage. If you have solar, the control panel is a good way to do this. If you have no solar, the other panel is ok. A multimeter is best if you suspect a problem. If you get below
12V, that's not good.
Lots of possibilities
Bob