Install the latest iTunes on your home computer. Authorize it in the iTunes store with the same account you have on your iPod. Connect the iPod BUT DO NOT SYNC. Go to the File menu and choose Transfer Purchases... This will transfer your apps and any iTunes purchased music and videos to iTunes on your home computer.
Now you can sync; the sync will delete content from the iPod, but since it is now in iTunes on your home computer it will be restored as part of the sync.
Have you tried Apple online support?
You can use or sync your purchases from the iTunes Store on up to five different computers (these can be any mix of Macintosh or Windows-compatible computers). When you sync or play an item you've purchased, your computer is "authorized" for purchase using your Apple ID.
Note: Songs you encode in AAC format from a source other than the iTunes Store, such as your own audio CDs, and iTunes Plus content (music and music videos) do not need to be authorized.
Q: Would you patronize a streetwalker?
A: No, I would treat her as an equal.