The conclusion of a solution for battery cable problems
1)Only the brown connecter was broken
You should order a new part this site, and reinstall it.
Then it could be OK, and your iPod would be resumed.
When a white part have been removed from the logicboard.
(Very serious problem, no adhesive can help this problem.)
A situation is told to below by e-mail or Fax, and you send parts, and have you solder to a logicboard again.
271, Ohhagi-Town Higashiohmi-City Shiga-Pref. Japan
Postal code 527-0174
Also I introduce this company homepage and weblog.
"Re-soldering of the connector which has taken the ipod board"
Sorry, although it is a Japanese site, but I think that it turns out that I introduce if you have a photograph and movie seen.
I think that there is no company which has the technology so far in the world as far as I get to know.
Do not give up, Good luck and God bless you.