Has your fridge ever worked on 240v mains? If so, you are either looking for a faulty change over switch, blown fuse or damaged supply cable. There is also the possibility that the 240v heating element is damaged or blown. A bit of continuity circuit testing should eliminate most of the above.
Your fridge should not be running off your vehicle battery with the engine stopped. The power drain to the 12v heating element is high enough to flatten a battery within a few hours. It is not linked to your first problem
Cledlyn
August 2008