Does it charge when you connect it to your PC? Are you plugging the iPod into a high powered USB 2.0 port on the back of the PC instead of plugging it into any sort of USB hub or even a USB port on the front of your PC.
It might not hurt to also try another dock connector cable as well to help rule out a faulty or damaged cable.
Has this iPod ever successfully connected to this PC and iTunes? If so, what has changed since that happened?
Perhaps this article can be of assistance.