Try restoring on another computer, or, if you don't have access to another computer, create a new administrator account independent of other users, install a fresh copy of iTunes, and try.
I already have done that because the adhesive on the back of the battery had stopped sticking and phone would turn off whenever I bumped it, so I applied more adhesive, reassembled and it was fine for about a day and then it just turned off and wouldn't turn back on
I don't believe Apple still services the 3GS but you can try bringing it to an Apple Genius Bar and have them run diagnostics on it and see if it's salvageable. More than likely it's a logic board issue since taking out the battery didn't assist the issue
I live in new zealand, and and unfortunately, there is no such thing as an apple genius bar, so I guess it's the trash for this one. Might just take it apart one more time to see if there is anything wrong I can see.
How long should I leave the battery out willerz2?