Reconnect battery plug to the logic board of an iPod classic?

Big Guy, that is a very common thing to happen. Anyhow, there are really only a few things that you can do. One is, of course, to replace the logic board. Not a very expensive or difficult task. The other thing you can try, is to get a local shop to solder a new connector onto the board. It is surface mounted, so you will need to get someone with experience in doing that type of repair. Check this video and see if you might be up to it. The clip is available at places like this.