What internal connector are you referring to, the DC connector, or the battery connector?
You can't wire a battery directly to the charger. Charging a Lithium-Ion battery requires a somewhat complex charging control circuit. Well, I shouldn't say you can't; you can, you just run a really high risk of blowing yourself up.
If the mobo traces are broken in a visible area scrape the insulation off of the pcb and solder a heavy gauge wire to the surface to bridge the trace. I'm not sure of the repair method for the inside layers of multi-layer circuit boards.