It sounds as if the power is getting to the fridge, but the heating element is not working. It is situated next to the flue, if you can get to you can tell if its working by putting your finger on it {carefully} to check if its getting hot. If not it is reasonably easy to fit a replacement, at the last quote they were around £30. I am not a fridge engineer, this is only what I have found out by experience. Good luck.
Ray, May 2010