As lllaass said, Apple does not repair iPods, but will replace the entire iPod for a flat fee; see the Repair Pricing section here:
There are no discounts on out-of-warranty exchanges for anyone.
There are independent iPod repair services that may be able to replace the screen for less. Do a web search for "ipod repair". Note, though, that if you elect to have the iPod serviced by an unauthorized shop, all further warranty will be void.
Message was edited by: varjak paw