It's possible there's a fuse to check. It's more likely the thermostat has failed. A quick check (not infallible) is to rotate the thermostat control and listen very carefully for a 'click'.

If you do hear this it means that it is at least trying to switch the compressor.

If you don't hear a click then the compressor isn't being switched.

This click may be very quiet, but not neccessarily. Different models have different thermostats whic have different clicks.

Depending on your results, check to see if there's volts at the compressor (get someone who knows a bit about playing with mains voltages). The compressor may well be quite literally a black metal box with wires and a pipe or two leading to it.

If you get volts and you can't hear the compressor making a sort of whiring buzzy sort of noise then it may be knackered. Check to see if the compressor is very warm.

If the compressor is goosed it's probably worth checking out a replacement fridge. I wouldn't have though compressor replacement was economic, unlike thermostat replacement which is a doddle. And cheap.

Another possible cause is the refrigerant gas has leaked out. The hole needs to be found, repaired, then the whole thing recharged.

I hope this helps you. Good luck.

John