When a battery positive melts/burns it obviously has touched ground. The damage to the hot wire will only be as far as the ground source. If your dash wiring melted there are only 2 sources coming through the firewall. The black wire from the alternator output stud. And the blue fusible link from the starter relay. This wire is red on the inside of the car. If it didnt burn the fusible link the issue is in the black wire circuit.The black wire has splices feeding various items in the dash. The ignition switch, headlamp switch, horn relay, fuse block, and ammeter. Follow the melted black wire circuit under the dash until the wire isnt damaged. At that point you'll find your issue.
Doug