Miles; THE GFCI's in the trailer may be tripping as Gary and mainah stated.
As for the Fridge;
Get the model # off the refridgerator, and take a picture of the area inside the door, pay particular attention to the wire connections on the fridge frame. POst them. There should be 12V lines coming in to the left bottom along with the 120V lines (which means the fridge won't work in GAS MODE with out a battery hooked up to power the board in gas mode.) You need a battery anyway. A 24 or 27 series Deep Cycle Marine/RV will do the job. Get the battery and 12v working, then run the fridge on Gas. It should (if working and most times do) start cooling the freezer in 2-3 hours and the chill box in about 8-10. The fridge does not have a compressor, running on a heat/cool closed cycle.
https://lifeonroute.com/rv-fridge-works/
Give it 24-36 hours to cool down completely. Temps with a manual thermostat set to max should be about 15*F in the freezer and 37-41*F in the chill box. Keep a charger maintainer on the battery while not hooked up to landline while you're working on the 120V.
Replacing the whole refrigerator is prohibitively expensive. A new coil unit is about $550-800, depending on who you get it from. A new electronics control board runs from $100-200, again depending on who/where you get one from. If you need a new control board, DINOSAUR ELECTRONICS make one of if not the best lines of control boards, and cheaper than a Dometic/norcold board. If the physical unit is intact, fairly clean in current condition, and intact, keep it.
Troubleshoot the electrical problem, ensure the fridge works on gas (once you get a new battery(and a marine box to keep it in), then troubleshoot the electrical system on the fridge. It's fairly simple.
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