First I would try to reset the mini with iTunes. Just to make sure you have the new firmware for your device etc. Make sure all your data is backed up when doing anything on the iPod. So reset it by
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.
If that does not work and you can't get into diagnostic mode or disk mode. I would disassemble the iPod and check that all cable are connected and that all connection and cables are free of corrosion. If all that check okay I think it is time to replace the click wheel. iPod Mini Click Wheel Replacement shows you how to do it and the part is available here iPod Mini Gen 1 Click Wheel of course make sure that these instructions and parts are for your generation of ipod. Good luck to you and let us know how it is working out for you.