Hold the Sleep/Wake and Home buttons together until you see the Apple Logo or it shuts off, then turn it back on. Then try again in App Store Updates. Let me know.
Ok there is really no iTunes for iPod do you mean Music ? If there are no Updates in the App Store then you have the latest version of Music on the iPod already.
So you are referring to iTunes on your computer right not the iPod??
Please go to the Apple logo at the upper left of your computer screen to About This Mac and give me this information:
Restart the HP and then do not open anything else and go to Start / Apple Software Update and try again. If you still have problems when you go to Apple Software Update select the iTunes update and then go to Toold / Download Only