The "Do not disconnect" on the iPod's screen is a good sign. That means the iPod has a data connection, so the cause is more likely to be a problem at the computer end of the connection, related to iTunes or Windows.
If you have not already, try downloading and installing the latest version of iTunes (if your PC runs Windows 7 or later), from here
https://www.apple.com/itunes/
The background processes that identify when an iPod is connected may not be running properly.
If that does not help, as a test, try shutting down (powering off) your computer, and disconnecting all USB devices. You can leave standard USB keyboard and mouse connected, if used. Do a Reset on the iPod
Learn how to reset your iPod - Apple Support
Start up computer, run iTunes, and connect iPod (not in Disk Mode at this point) to a direct USB port on the computer. Try more than one port.