"Do not disconnect" on the iPod's screen good. It's also good that you briefly did see it in iTunes. I think the data connection is working, and the iPod is probably OK, but there is a software issue on the computer.
As a test, shut down the computer and disconnect all USB devices. You can leave standard USB keyboard and mouse connected, if used. Do this to Reset (restart the iPod)
Learn how to reset your iPod - Apple Support
Start up computer, run iTunes, and connect iPod to a direct USB port on the computer by itself. Is there any difference?
If that does not help, I would try reinstalling iTunes by downloading the latest version here
http://www.apple.com/itunes/
Your iTunes data is not affected by reinstalling iTunes, but you should have a backup (which is good advice whether you are reinstalling or not).