Does the iPod function? If so, in the device's settings you should find an About page which displays the SN, and iTunes (or Finder) should display the SN in the device summary screen. Double-check to make sure you have the correct SN with no typos.
EDIT: I entered the SN from my old iPod photo into the coverage page and it failed due to my mistaking a 5 for an S. After correcting that and trying again, it displayed the model number and the year I purchased it.
If you have a dead device and you're trying to read the the SN from the printing on the case, I hope your eyes are better than mine. The small text on my 7th gen Nano is unreadable even with a strong magnifying glass.
You could try posting a photo of the iPod here.