@mithrilll sounds like your firmware got messed up. Just running it through iTunes probably wouldn't have fixed it. I would have suggested to reinstall the firmware. After downloading the proper firmware, you can shift-click (PC) or option-click (Mac) the ''Restore'' Or ''Update'' buttons in iTunes. That should have opened a dialog box where you choose the proper ''ipsw''-file. You can download that [https://archive.org/download/apple-i-pod-mini-a-1051-v-3.1.4.1-firmware/Apple%20iPod%20Mini%20A1051%20v3.1.4.1%20firmware.zip|from here]
You will also have to place the iPod into disk mode to reformat to FAT32. Reboot the iPod by sliding the Hold button back and forth, then pressing Play/Pause + Menu. When the Apple logo appears, release the Menu and Select buttons and immediately press and hold the Select and the Play/Pause buttons until the Disk Mode screen appears. of course, you can also check the [https://www.youtube.com/watch?v=WTPZf_oe6g4|this video] for the how-to