Have you been using the same cable or a different one with the different charges. If the same cable try a new one, there have been issues with defective cables. Try the cable first. If still no joy, have you tried resetting your iPod? Press and hold both the power and home buttons together until the Apple logo appears (about 15 second) then release both. Or go into Settings>General>Reset>Reset All Settings. (Could also try letting your iPod drain down to zero, then attempt to charge, but you have already done that.) If all else, you can contact Apple Genius Bar about it, your under warranty, why not use it. Hope this helps, Good luck.
- Try another cable. Some 5G iPods were shipped with Lightning cable that were either initially defective or failed after short use. I suspect a bad cable
- Try another charging source
- Inspect the dock connector on the iPod for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic.
- Make an appointment at the Genius Bar of an Apple store. The cable as well as the iPod is covered by the one-year warranty.