Connections were/are loose. If it's a main lead between the switch and fuse holders replace with same size wire. Should be able to get some at local home improvement store. Get stranded not solid wire THHN, THWN or equil. Most likely fuses are fine. Check all the connections for tightness, they will come loose after a while from the constant expanding and contraction from the heat. Take it a step further pull all the main leads one at a time and make sure they are not corroded or burnt. From what you are describing the wire was loose, generated heat and finally melted down.
Pick up an inexpensive multi tester if you do not already have one. Set it to ohm's (omega symbol), remove each fuse and touch the test leads to each end of the fuse. A digital meter should read "0" for a good fuse OL for a bad one, analog needle should move all the way to the right for good, not move for bad. Do not hold the metal part of the probes with your fingers, you could get a false positive, your body is a great conductor.
