Check any fuses/circuit breakers in harness from battery. That battery should supply 12 volts dc to fridge lugs/terminals at bottom of fridge on outside behind vent.
If battery is good and hooked up properly but no 12 volts to fridge, then you will have to trace back to battery for broken /bad wire. If you want to test quickly, just run 2 jumper wires from battery to those 2 lugs marked + and - Battery + to + (pos)at fridge, and - battery to -Neg at fridge. That should allow you to run it on propane or 12 volt. Remember, running it on 12 volts will kill that battery pretty quick, unless it's being charged. When you are plugged in, the converter supplies the 12 volts to your fridge, as well as should be charging your battery.