Hello d,
These multi fuel fridges all work on the absorption principal where to make them work you actually have to heat part of the refrigerant system. This means you can have gas, mains or 12v heat sources.
The good news is that if it works on one fuel type, it proves that the refrigerant system is intact.
You say the pilot light is on, and for clarity are you referring to a visual sight of the flame through the transparent plastic rod? - if so then it should be a nice irridecent blue flame.
The flame you see is not just a pilot, it is the main flame, and if it is present, and the fridge is not working then something is wrong in the burner area.
As with all gas appliances all installation, service, repair or removal must be carried out by a competent person working to the gas regulations.
I think you need to referthe caravan to your service centre.