Try this to et the iPod working so you can find the SN via setting
Try:
- iOS: Not responding or does not turn on
- Also try DFU mode after try recovery mode
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.
- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.
Apple Retail Store - Genius Bar
Try shoe polish or other media on the back of the iPod to try to make the engraved SN readable.