Most probably the thermostat. If you understand electric circuits and I tell you that the thermostat is in series with the compressor, then you will realise if the thermostat dies then the compressor stops! If you can follow that then you may feel able to - unplug the appliance, find the two wires to the thermostat, disconnect them and short them together and then plug the fridge back in and turn on. If the compressor runs then you've found your problem - and your solution, a new thermostat. If it still doesn't work then it could be the compressor, but they usually last for many years - unlike thermostats!
Richard, January 2009
