How to charge the battery if the power input is damaged?

The mains power socket on my Satellite 4070CDT has been damaged and the laptop will no longer take power or recharge the battery from this socket. (Attempts to re-solder the joint have damaged the power detection circuitry!)
Does anyone know if I can feed the appropriate voltage (10.8v?) to the battery contacts inside the battery housing to keep the laptop going, and if so, which contacts and with what tolerance on the voltage?
(Applying 12v across the +ve and one particular -ve contact seems to persuade the power management software that it is running from mains without a battery, but after 20 seconds the laptop powers down.)
Any ideas? Thanks.

With some experimentation (and the assistance of a voltage meter) I have found a solution, which I have described below should anyone else be similarly troubled!
My li-ion battery has 10 end-facing contacts and 2 top-facing contacts. One of the 2 top-facing contacts is the real +ve contact for the battery, which passes charge via the other top-facing contact to the end-facing contact that is marked as being the +ve terminal.
Of the 9 remaining end-facing contacts, only two (the 3rd and 10th counting from the +ve as 1st contact) were reporting any charge, probably due to the battery being almost fully discharged.
I have soldered the 12v +ve supply from a new external adaptor to the 1st end-facing contact (which is marked as the +ve contact) and the -ve connection to the 3rd and 10th contacts, feeding the cable out through a notch cut in the laptop casing at the contact end of the battery.
The cable is terminated with a suitably sized floating socket to receive the plug from the 12v adaptor.
AND IT WORKS!
The laptop is reporting that the battery only has 4% charge, but it keeps going! I have turned-off the battery alarms and system-tray indicator as they are meaningless now.
So my 6-year-old laptop lives to see another day, although it is no longer a 'mobile' device now that it needs constant mains supply - but it still has its uses.
Query closed!

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