Hello Teddy
Usually when a fault arises, you have to follow the symptoms and work back to find what actually caused it. Without testing we simple can't confirm or deny if fault in the fridge is simply a component aging and failing on the PCB, or whether it's been caused by something external to the fridge. The 13pin plug is just one possibility as there are several components between the fridge and the power that runs it, it's possible it could be any of them.
However I cannot think of how a fault on the 13 pin plug would be able to cause the PCB in the fridge to fail. If it were just loose connection in the plug the fridge might stop working. If the wires were shorting in the connector you would have other symptoms, like other things not turning off or blowing fuses.
I have had to deal with a German caravan where the fridge PCB was damaged, but that was because the cooker above it had not been correctly wired, and the cookers spark generator was putting 15Kv through the fridges pcb. But that is not suggesting its the same as your problem.
I'm sorry but in situations like this it needs hands on attention by someone who is competent at fault finding.
Having said that there is no harm in checking the 13pin plug for loose connections if you fell up to the job.