Check the power plug for the unit. Ensure that the outlet is a good and that it can handle the voltage of the refrigerator.
Inspect the circuit breaker of the home and check for flipped switches.
Unplug the unit for 24 hours then plug it back in. If the unit turns on, the compressor is shorting out once the unit warms up.
Pull the unit out from the wall to expose the back of the unit. Kneel down to access the compressor and the overload protector. The overload protector is a small metal box that has wires going inside.
Pull off the cover of the overload protector and inspect the wire connections for corrosion. Pull up on the spring clip holding the overload protector in place and pull it out.
Set a multimeter -- a device used to test voltage -- to the X1 setting. Touch the multimeter to each probe of the terminal. You should receive a reading of zero ohms. Replace the unit if you receive anything other than that reading.