Like I mentioned earlier, the trick to make it work, would be to use the compressor/heat exchanger to cool a liquid, not the inside of the fridge.
The system essentially works like this; the compressor compresses a gaseous refrigerant which causes it to rise in temperature. The refrigerant, still in gaseous form and under high pressure, is sent to the condenser (a heat exchanger) where it is cooled down and condenses into a liquid (this is the phase change that occurs). The now liquid refrigerant is forced at high pressure through copper capillary tubing into an evaporator chamber which is a low pressure area, and evaporates back into gaseous form, absorbing heat in an endothermic reaction (it gets very cold).
The evaporator chamber in the system we are talking about is essentially another heat exchanger, allowing antifreeze laced coolant to be pumped through it, without contamination from the refrigerant. This in turn will be pumped through waterblocks on the CPU, Northbridge and the VGA card processor, in the same manner as a standard water cooling system. The advantage of the Phase Change system is that the evaporation chamber internal temperature will be about -40 degrees centigrade, giving a coolant temperature of between -15 and -30. This in turn will give a processor core temperature of about 0 to -10 degrees, (hopefully).
If you already have the fridge, £250.00 would be enough to sort out a good water cooling kit, and the evaporation chamber. Be aware that the refrigerant chemicals are quite unpleasant, and you don’t want to be letting them out.