I recently purchased a 1996 Audi A4 2.8L. When I bought the car, the guy told me the headlights recently went out. I didn't do very much investigating then because I figured it was blown bulbs. I found that it is not the bulbs, but a bigger electrical issue, and I am not very good with electrical.

The low beams on the car do not work at all, nor do the high beams when they are in the locked position. The only head-lighting that works is when the high beams are pulled back, as if to flash someone. However, when I turn on the low beam lights, the interior lighting turns on, that which is typically supposed to come on when you turn the lights on in the car.
Along with these issues, the exterior markers do not work, but the turn signals do.

I have done some research and found that the multi-function switch has been known to melt and get between two contact points, causing a lighting problem.

I also in doing investigation, found that the fuse box has places where it has melted (specifically the points for the rear and side marker lights, just by the low beam headlight fuse spots).

My questions are these: one, what is the best DIY for the fuse box (any help getting me a link to follow to a procedure, etc); and two, does anyone have any further advice/ insight regarding my lighting issue, that might not stem from the fuse box issue?

Thanks so much!