Does iTunes open and run properly when the iPod is not connected?
On the "other" computer (where the iPod was recognized properly), did you use the same USB docking cable?
If YES to the above, since you said the iPod is recognized properly on another computer running iTunes, and the iPod itself works properly (as an iPod) when disconnected, the problem is likely to be on your computer. It seems to initially recognize the iPod (because the iPod appears in iTunes), but then something causes iTunes to "hang" when trying to access the iPod.
As a test, shut down the computer and disconnect all USB devices. You can leave standard USB keyboard and mouse connected, if used. If your computer is a laptop, connect its power adapter so that it's not running on battery power. Do this to Reset (restart) the iPod
Learn how to reset your iPod - Apple Support (see section iPod with a click wheel)
Start up computer, run iTunes, and connect iPod to a direct USB port on the computer, by itself (using the USB docking cable you used with the "other" computer). Is there any difference?