iPod Touch iOS 4 to 6 update problems

I recently tried to update my iPod Touch 4G to iOS 6. I originally tried it on a newer computer, not the original computer I had synced the iPod to. I saw that it would delete the apps and music because this was not the original computer, so I backed up my iPod and transferred the purchases. However, whenever I click on an app in iTunes, I get the message "The app --- can't be used because the original file could not be found. Would you like to locate it?" When I try to locate the app, there are only a few apps that are actually in the folder.

Then, I went back to the original computer. When I tried to update the iPod, it started to back up very slowly. When I came back a little later, nothing was happening, and the backup icon had disappeared. When I clicked the update button again, it started the same process. When I Googled that, it told me to restore my iPod. I would do that, except it had stopped syncing to the original computer, and because I'm not sure if the apps are on the new computer, I don't want to take the chance of losing my apps.

It appears that I am stuck in sort of a paradox. Help!