I just went through the same problem, called 1-800-MY-APPLE and had the issue solved in less than 5 minutes.
If your iPod has been synced with itunes, it is very easy.
From your mac, open itunes.
go to the itunes menu bar at the very top of the screen (not the itunes window).
Select itunes, Preferences. A window will open up.
Click on the devices icon at the top of the window.
Find your ipod on the list, then hover your mouse over it. Your serial number will display.