I would start with
New cable and different USB port?
Runs this and see if the results help with determine the cause
Try on another computer to help determine if computer or iPod problem
-Did you try another cable?
what did this show?
- Run this and see if the results help with determine the cause
- Inspect the dock connector for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic.
- Make an appointment at the Genus Bar of an Apple store.
That is likely the problem.
Apple will exchange your iPod for a refurbished one for this price. They do not fix yours.
A third-party place like the following is less. Google for more.