Chosen Solution

The ipod won’t sync or charge, but it will play on my stereo. There are no problems with the usb connection, as I can connect my nano.

What I would do is to replace the battery. Without any damage to the iPod, and a dock connector that is free of dirt, debris, corrosion etc. it is possible that your iPod does not charge through the computer and will not be recognized due to a dead battery. The dock provides a higher amperage than the computer. Of course, do make sure that your dock connector on the iPod is a-ok. Hope this helps to get you started.