Old mini-fridge, suddenly stopped working, please help!?

I obtained an old mini-fridge from my grandmother, and it has worked perfectly. I cannot seem to find any identification on the brand of the fridge, but it does have a wood finished siding on it. My buddy recently pushed a white on located on the inside of the fridge, and it just stopped working. The on is sticks out of a black dial on the upper right side of the interior of the fridge. The dial has marking on it labeled as; "stop", "min", "med", and "max". I have tried turning the dial into different positions(which is really hard to do, because the dial is so hard to turn), i have tried unplugging the fridge and then plugging it back in, and i have tried pushing the white on again. Nothing that I try seems to help. There does not appear to be anything on the backside of the fridge that I can change. Please help me, I do not want to have to buy another mini-fridge. I will award best answer to the person who provides the advice I need to fix the fridge.