The battery uses a special pinout - trying to re-wire it without a schematic is a good way to fry your system.
If you can find some way to connect your jack to the leads that are on the board, you can get it back up and running. I've encountered this situation once in an older Dell notebook, where the board underneath the DC jack was a peninsula of sorts; the user had dropped it and broken the piece off the board. I wasn't able to fix it, though I only spent a few hours on the machine.