Generally, if a three-way fridge isn't working on one power source, try it on the other two.
If one or more works, the refrigerant is OK.
If it's the mains not working, it's probably the heating element (cheap to replace).
If it's the 12v not working, it's probably a wiring,
fuse or relay problem.
If it's the gas not working, it's probably a partly blocked jet. They're tiny and block easily.
If it's the gas not staying lit at all, it's probably the thermocouple worn out or wrongly positioned (or the burner is dirty).
Also check that a spider hasn't blocked the flue with a nest.
The only expensive but likely fault is a blown control board. These tend to be damaged by unplugging the hookup when mains powered fans (usually fan heaters or aircon) are running: the voltage surge from the spinning motors destroys the fridge electronics. And it costs a bomb to fix. Always switch stuff off before disconnecting hookup.
If it works in cold weather but not hot, it's not getting enough circulation. Remove the vent covers or fit fans.
Turning the fridge down (to less cold) will help by making the cooling task less energy-consuming.
