Ellis, since changing my car i have found that my fridge also does not work on 12 volt although the light comes on as you state. as an ex refrigeration engineer i tested the fridge to find it was all fine, i then found that the tow bar fitter had wired the charge and fridge circuit up to my rear auxillary power socket on the car, unfortunately this is only fused at 10 amp but more importantly has on 1mm gauge cable. what this meens is the when the fridge draws power the cable is not large enough to provide the power needed so the voltage drops to a level lower than what is required for the habitation relay to switch over so the fridge will not work. some can hear this relay clicking in and out, i can't, like me you may need to get the charge and fridge circuit taken directly from the battery as it should be and ask for suitable diameter cable to be used. obviousley you may have a faulty fridge but it sounds to me like you have the problem as me.