firstly - make sure that the thermostat bulb (the long metal tube) that comes out of the thermostat switch and into the fridge, is firmly in contact with the evaporator (the cooling plate) inside the fridge. If the end of the thermostat tube is not fully in contact with the evaporator then the thermostat will be unable to read the temperature within the fridge and as a consequence the motor will be constantly running.
If this is not the problem then replace the thermostat .This is not a difficult job but you must be careful not to kink or break the thermostat bulb (tube). And remember that it is very important to ensure that the thermostat bulb (tube) is firmly in contact with the evaporator (cold plate)
neil rogers, October 2005