If it was me, I would find out which contact this burnt lead is supposed to go to and run a small wire from the solder joint of the white connector (from the front side) straight to the blue surface mount capacitor(?) that the trace goes to. Looking at it up close, the blue 'covering' goes near flush to the pcb, so this might be difficult to do, if it can be done at all.
The only other options I can see that are available would be:
1)Get a new filter board (the pcb you are holding in the pic)
2)Get a new/another Naomi (to replace current board; non-working system for parts)
3)Send it for repair. (
www.irepairsega.com -- Ken Westerfield is awesome!)
I'd say #2 is the fastest, most available option. Getting a non-working Naomi for the filter pcb wouldn't be hard.