If the wire you mentioned burned up like that, you have a nearly dead short in one of the circuits fed by fuse 13. If you don't have one, get an inexpensive digital multimeter, about $10 bucks at Harbor Freight for example, and do some troubleshooting with it.
1. Disconnect the battery
2. pull fuse 13
3. measure the resistance from the output side (right side,I think) of fuse 13 to the chassis (ground). I would expect the resistance to be less than 1 ohm, probably nearly zero due to a short in one of the wires being fed from this fuse.
4. Pull the wires off one at a time and check the resistance of that wire to the chassis. If you find one which is nearly zero ohms to ground, you have found the bad circuit. If you have a wiring diagram, the color of the wire will help you to figure out what that wire powers and you can start looking for the problem. Or, you can post the wire color here and someone will look it up for you. Be sure to tell us the year of your car.