Dometic RM2852 Fridge Won't Cool

check your 12v battery, either on propane or 120v it still needs 12v .

When it's not working on 120v power, does the boiler on the back get hot? If the electric elements are working, the boiler on the back gets very hot. Either the propane flame or the electric heaters have to produce heat for the system to work.

Start by trying on propane. It should show cooling in a couple hours.
Yes, they had problems with the relay to power the 120 volt element.
If you have a multi-meter, locate the wires coming from the stack for the 120 volt element. Disconnect 120 volt power by un-plugging the refer. Disconnect the wires going to the element. Set meter on resistance. measure the wires to the element. You should have resistance.
Next, plug the refer back in. set refer to AC, test the terminals where the element connects. you should have 120 volts.
Order an new Dinosaur Electronics circuit board.