If it is a Dometic refrigerator, then it is very unlikely that you have any sort of a "compressor" as most, if not all, of them are absorption based with no moving parts at all. How is the charge on your battery? The control board in the fridge is run from 12 volt battery, though some use the converter when the battery is weak. More specific diagnostics will follow from someone soon I'm sure, such as checking the voltage through the 120V heating element, etc.
"Sometimes I just sit and think. Sometimes I just sit." "Great minds like a think."