If Apple determines that an iPod is not repairable, for example, if it has failed due catastrophic damage or the iPod has been disassembled into multiple pieces, then Out-of-Warranty Service is not available and the iPod will be returned. Please see Apple's Repair Terms And Conditions for further details.
Apple will exchange your iPod for a refurbished one for $199 for 16 GB 4G and $99 for the other 4Gs. They do not fix yours.
This is an out-of-warranty repair so no warranty is required