Quoted from Quench:Is the grey wire melted going into the transformer? If yes, I would slice the external transformer paper to access the lower grey wire solder joint on the transformer and replace that melted grey wire altogether and make sure all other wires are properly insulated from one another. Then repair the sliced transformer paper. I'm not sure how comfortable you are doing this though..
I agree, I wouldn't pitch the transformer, I would go back as close as you can to the transformer and solder a new wire or wires in place.
The fuses for the wires that lead to the sound card are on the sound card itself. Since the wire burned, I would check the values of the fuses on the sound card (and all others in the machine if you haven't yet) to make sure the correct values are installed. Its possible the wiring running through the backbox shorted to the backbox metal shield somewhere or got pinched under a screw.