When sdagger comes back with the requested information we may be able to work out how to get him to disconnect the Peltier device. I am reluctant to suggest unsoldering one of the wires from the PCB to the Peltier device as we don't know his ability at soldering.
Hi all. I think i'm too scared to even think about taking things apart further. I'm guessing this should just be scrapped as I don't want to electrocute myself trying stuff above my head?
If you feel confident with your soldering, you could try -- having made sure the fridge is switched off and unplugged -- removing the crimps (circled in green) from these wires:
(If you're confident you'll be able to solder them back together properly later; or obtain some new crimps and recrimp them.)
Set your multimeter to the lowest resistance setting -- it will be labelled something like "200 Ω"
or perhaps just "Ω"
And then test the resistance across the two wires coming from the Peltier unit.
If the reading is in the low ohms -- say 3.0 Ω ... 8.0 Ω -- then the Perltier unit is probably okay, and it would one or more components on the board that is at fault.
At that point your best course of action would be to take some good -- well lit, in focus -- photos of both sides of the board and post them here; and perhaps the experts here will be able to talk you through diagnosing the fault.