What model frig do you have? Is it a 2 way (LP / 120V ac electric) or a 3 way frig (LP, 120V ac electric / 12V dc electric)?
I am not familiar with the DC option. Hopefully others can chime in.
Have you removed the outside cover and verified you have power at the 120V outlet? If no power and you are connected to shore power, verify GFI outlet inside the PU has not been tripped. Also check the circuit breakers within the PU.
Have you tried running it on gas? It can take a few hours for the frig to cooling down. Most often it is best to first light the stove to ensure the gas line is purged, then the other items within the camper.
If it works on gas, and not AC, I suspect the electric heating element is shot, Not an expensive part. On a PU I am not sure how hard it is to replace. On a TT like my 8cu frig, I have to pull the frig out of the frame to access the location on the backside.
As for running the frig while going down the road. Not an issue for the frig. Running the frig and having the PU sitting idle out of level, is not good. Most older RV frigs can be out of level by 2 degrees side to side, and 4 degrees front to back. Newer frigs can be 3 degrees by 6 degrees out of level.
The ammonia gas in the system uses gravity in order to work properly. If it is sitting in your driveway, way out of level and running. The system can overheat, ammonia crystals can form and block the passages (kinda like cholesterol in your arteries).
If I was a beating on the root issue, it will be the GFI outlet is tripped or a bad electric heating element.
Good Luck, let us know what you find.