I believe the cables are the same for all iPods/iPhones, at least for connecting between the USB port and the iPod. The drivers for the computer are installed as part of the iTunes installation. In fact, I think it is the same Apple mobile device driver.
Here are some ideas I would try: First, are you sure the docking port on the iPod itself is working. The easiest way to test this would be try the iPod on some device that has a docking connector, such as a pair of portable speakers for the iPod. If they don't work, then I'd suspect the problem is in the docking connector.
Next, I'd make sure the USB port I was using was good. Connect another USB device there, and see if it works.
I'd make sure the iPod was charged. Using an external charger is a good way to test the cable.
If those are good, I'd do a fresh reboot of both the windows system and the iPod (flip lock, hold select and menu). The windows driver could just be wedged. Then try reconnecting.
If you still get nothing, two other options. First, replace the cable -- perhaps a wire is bad. Second, run diagnostics on the ipod. If you do a google search on "ipod classic diagnostics mode", you should get instructions on how to have the ipod test itself.
I hope this helps (from one layperson who loves their ipod to another).