Ugh, most likely low or out of refridgerant or compressor has internal problems. I have found in most cases it's too costly to mess with the sealed system and you would be better off with a new fridge. You could ohm out the compressor but it would just be a verification of the problem.
Ohm 1)C to R; 2)C to S; 3)R to S; 1+2=3; Ohm each to compressor housing should read open if not it's grounded to the housing.
Perhap's one of the tech's with more HVAC history would have an economic solution...but if it were my service call I would most likely condemn the machine. Sorry.