how hot is the compressor when its running? The fan went out on one a fridge of mine once, I saw that the fan was out. I just put a small fan down there blowing on the compressor and it started to work. gave me enough time to remove the broke fan and replace it with a new one.
Most likely starting components went out on compressor. You can get a 3 n 1 start kit from a HVAC parts wholesaler like Baker Dist or Johnson Supply. They don't cost a whole lot ($20-$40) and easy to install.