Since no one has responded yet. I thought I would try. Please understand that I am not an expert, by any means.
I would first unplug the refrigerator, and, just as a test, "jump" the broken wire(s). That means stripping the insulation from the broken ends of the existing wire. Then, get a short piece of wire (jumper wire) and strip the insulation off the ends of that jumper wire. Use wire nuts to connect each end of the jumper wire to the broken ends of the refrigerator wire.
Then, plug the refrigerator in, and see if it goes on.
Post back to let us know if that worked.