Are you talking about 12v or mains EHU? It will only work on 12v when connected to the car with the engine running, I believe. If you mean EHU then you need to start off with fuses or bad wiring I would suggest.
Could be the heating element gone. There will be a 240volt one and a 12volt. You can access the fridge by removing the external vents then undo some screws and it draws out into the van. Test the elements with an ohmmeter.