Start by looking at all the connections and ensuring that the mains, 12Vdc and the gas are all available.
It would appear from what you are saying that there is a problem with the supplies in the caravan rather than a problem with the fridge.
Silly question. I take it that you have connected the caravan to the mains via the cable and the caravan battery is fully charged and supplying volts. By the way, it is not a good idea to operate the fridge from the caravan battery. The fridge takes a lot of amps and will drain the battery in double quick time. The 12Vdc for the fridge is meant to be supplied from the car when the engine is running.
Ok. We have established that we have the different power sources on the back of the fridge.
Was the fridge working earlier in the season? What was the reason for taking it out?
If, as you say in your original post, it worked in the house, provided all the necessary supplies to the fridge are connected and you have established that the necessary volts are there, I cannot see a reason for it not working other than an air lock in the system which has been caused by the fridge being moved about from the house to the caravan.
When you switch the 230V mains and the 12vdc on on the control panel, do the lights in the switches light up?
If they light up, is the mains temperature control set away from its lowest setting, say to about 5 or 6? If it is set on its lowest setting, the fridge may appear not to work. There is no control for temperature in the 12vdc mode. You get what it gives you.
If the fridge is controlled via a rotary switch so that you can switch between the three modes of operation, is the switch in the appropriate position for mains, 12v or gas?
If the answer to all of the above is yes, I regret at this distance I cannot offer any other solutions.