I had the same problem and was able to fix it. Here's the deal:
Everything worked fine until the iPod Touch was registered. Then two issues happened. 1) iPod Touch will not play "Protected" movies, videos, music even though all have been downloaded as "Purchases" from iTunes. (2) All Apps downloaded from App Store do not open.
The fix needs to occur with iTunes not the iPod touch. Here's what I did:
1. Disconnect Touch from computer
2. Reboot your Computer
3. In iTunes choose "Store" then "Deauthorize Computer." Enter your password.
4. In iTunes now click on a song from your music library (any song that you downloaded from iTunes and your computer will automatically "authorize" itself.
5. Connect the Touch and Restore to the original factory settings (not from a backup).
This fixed both issues. But be careful, I had to follow these steps exactly in this order. Where in previous failed attempts at fixing the Touch I had done everything listed above but not in this order.
More information can be found
http://support.apple.com/kb/TS1510