Have you tried a restore on your iPod?
That will take you back to factory settings, and you will lose any music and other files that you have on your iPod. You can then re-sync, and get your music back from your iTunes library.
It's worth a try, but likely isn't why you can't charge at all.
If your iPod still doesn't behave after a restore, try the restore a second time. If it still doesn't help, make sure that you have tried a second USB-dock cable. If you still don't get response, then your iPod has likely failed.
If your iPod is less that 12 months old, then Apple will fix it. Otherwise, repair (if that's available), or replace your iPod.