Just traces and fuses, right...no other components involved? Did you verify continuity from each pin to the end of its corresponding trace?

Also, with all that carbonization, make sure there's no shorts between the pins.

Looking at the schematics, you should have continuity on the following pins:

IN 1, thru F4, OUT 5
IN 2, thru F3, OUT 6
IN 3, thru F2, OUT 7
IN 4, thru F1, OUT 8

I could have my In's and Out's reversed, but you get the idea.

With a volt/ohm meter

Oh, I thought you already replaced the parts. Clean all the burned crap off and make sure all the traces are separated and solder on the new header, then test with the ohm meter.

Yeah you'll have to solder directly to the traces and you'll want to be a little more delicate taking the connector on and off, but it can be done. This is a single sided board so there are no thru holes to worry about. I would give it a try. If it doesn't work....well, a connector is cheap, a new board isn't.

Scrape the solder mask off the ends of the traces (which you will probably do in the process of cleaning off the carbon anyway.) Then tin the ends with a little solder. Put in the header and bridge the solder from the header pin to the trace. You may have to use a short piece of wire if the gap between the pin and trace is too great. Just make sure that if you use pieces of wire you don't end up shorting any pins together.

This isn't the best example, but you get the idea.

PCB3FourHolesSoldered.jpg