Like mattox said that is your problem. The backfire didn't burn the wire the burning wire probably caused the backfire.

The wire that goes to the choke control is also the same wire that powers the Alternator field, Ignition ECU and Ballast Resister which powers the coil. When that wire burns a lot of systems get shorted.

Basically everything that "turns on" when the ignition switch is in the run position is on that wire.

The only fuse for that wire circuit is the fusible link. Check it for damage.