The question doesn't really belong in the iSight forum--but, anyway, . . .
It used to be (and perhaps still is) the case that Apple put the serial number on the receipt if the purchase was made online through the Apple Store. Do you have such a receipt? Perhaps even an emailed receipt?
On a Mac, the serial numbers of all iPods ever connected to the computer get stored in a file. On a Mac, the file is ~/Library/Preferences/com.apple.iPod.plist. I would guess there's an equivalent file somewhere in Windows.
- If you previously turned on FIndMyiPod on the iPod in Settings>iCloud and wifi is on and connected go to iCloud: Find My iPhone, sign in and go to FIndMyiPhone. If the iPod has been restored it will never show up.
- You can also wipe/erase the iPod and have to iPod play a sound via iCloud.
- Change the passwords for all accounts used on the iPod and report to police
- There is no way to prevent someone from restoring the iPod (it erases it) using it.
- Apple will do nothing