My girlfriend was about to throw out her fridge because it had stopped working - so I had one last chance to tinker with it.
The fridge light came on, but the cooling mechanism didn't come on (didn't cool or make any noise)
Step 1: Examining the Thermostat
The Thermostat is inside the temperature adjustment box - I pulled off the box by hand.
The Thermostat contains an expanding copper pipe contraption, this pushed against a spring loaded metal plate.
As the pipe contraption warms, it expands against the metal plate and turns the fride on, as it cools the springs push the plate and the fride turns off.
There are a couple of screws that adjust the springs tensions, thus adjusting the temperature that that fridge starts up and turns off.
Step 2: Adjusting the Bite Point
It turns out the the plslate was moving correctly to turn off the fridge, but when moved to its most open position the fridge did not turn on.
This suggested a sticky switch, or that something had worn away on the plate not allowing the plate to quite turn the fridge on.
It turns out that a tiny set screw on the side adjusts the bite point of the plate operated switch, adjusting this resulted in the fridge working 100%