I cannot locate any parts for that unit or even that model number but it appears from your description that the temperature sensor has issues. I am not able to tell if it is a themistor, bimetal spring or capillary tube type. Which ever type it is, it needs replaced.
Need to know if the compressor motor gets power, does it heat up on top? If it does, then the motor starting device or a electric connection would be defective. If no power to the compressor and is ambient room temperature to touch, the controls are at fault, defrost timer, thermostat, connections. Work carefully around power, shock and fire hazard.
Please first check if the compressor is running or not, secondly check the compressor, piping for leakage of refrigerant. If there is leakage the must be some oil on the pipes just near to compressor.
If it is supposed to be frost free, then quite often, the drain outleft for the defrost water can be blocked, keeping the water inside the cabinet allowing it to refreeze.
