I think I would start with a new battery. After that I'd be resetting it under itunes
1. Toggle the Hold switch on and off. (Slide it to Hold, then turn it off again.)
2. Now press and hold the Menu and Select buttons until the Apple logo appears, which may take about 6 to 10 seconds. You may need to repeat this step.
or even trying to restore it to factory settings. Problem with that is that you lose your files (music) on the iPod.
Instructions from http://support.apple.com/kb/ht1339
1. Verify that you have an active Internet connection, because you may need to download new versions of the iTunes and iPod Software.
2. Download and install the latest version of iTunes if necessary.
3. Open iTunes. Connect your iPod to your computer using the USB or FireWire cable that came with your iPod.
4. After a few moments, your iPod will appear in the Source panel in iTunes.
5. Select your iPod in the Source panel. You will see information about your iPod appear in the Summary tab of the main iTunes window.
6. Click Restore.
7. If you are using a Mac, you will be asked to enter an administrator’s name and password.
8. A progress bar will appear on the computer screen, indicating that stage one of the restore process has begun. When this stage is done, iTunes will present one of two messages with instructions specific to the iPod model you are restoring.
- Disconnect iPod and connect it to iPod Power Adapter (typically applies to older iPod models).
- Leave iPod connected to computer to complete restore (typically applies newer iPod models).
9. During stage two of the restore process, the iPod displays an Apple logo as well as a progress bar at the bottom of the display. It is critical that the iPod remain connected to the computer or iPod power adapter during this stage.
Note: The progress bar may be difficult to see, because the backlight on the iPod display may be off.
10. After stage two of the restore process is complete, the iTunes Setup Assistant window will appear. It will ask you to name your iPod and choose your syncing preferences, as it did when you connected your iPod for the first time.
As for deleting or adding files to your iPod try un checking the "Sync Music" option, enable disk use, and manually put songs on oe delete them. Sometimes this can be cause by corrupted files on your nano and may disappear with the restore process.
After all these steps, reevaluate your nano and see what needs to be repaired. My motto is to never try to fix more than one error at the time, this way I know what needs to be fixed without losing track of it. Good Luck....