need help sync'ing iPod Touch (not authorized error)

I have an iPod Touch (about year old not sure if 4th or 5th Gen), iOS 8.1.2. I used to be able to sync everything fine with Windows ITunes on my old desktop, but when I got a new desktop I can't sync (more precisely I can't "Apply" updates to apps). When I go to the device's Apps tab on the left of ITunes interface, I click the "UPDATE" button on an app (Temple Run 2), it changes to "Will Update", then I click "Apply". During the sync it says

"The iPod "name" could not be synced because this computer is no longer authorized for purchased items that are not on this iPod. To authorize this computer fro items purchased from the ITunes Store, choose Store>Authorize This Computer."

I know this question has been asked by others, and I've tried many things including deauthorizing and reauthorizing, going into hidden files and deleting the SC Data folder, signing in with another of my ITunes accounts, using the "Manage Deivces" section of My Account, etc. None of it works. (Note: In Manage Devices, I see the iPod in question, but I renamed recently and it still shows as the old name in "ITunes Manage Devices" - I am afraid to delete it and add it back under the new name because I don't know what good or bad would happen if I do)

So, is there another idea out there? I would do a hard reset on the iPod, but I am afraid I;ll lose all the data for each app, especially game progress.

Any ideas to troubleshoot this?

Thank you,

Mike