first try plugging the iPod into the computer without the iPod on hold. Wait a little bit, about as long as it would take for the computer to recognize the iPod (it is ok if the iPod is not recognized). While the iPod is still plugged in, hold down the Menu Button and center button together for about 10 seconds, or until the screen turns off. The iPod will turn back on and the computer should recognize it.
Option two would simply be to wait until the iPod dies, and then plug it into a computer.
Once you try one of these (if it works), plug it into the computer and make sure that all software on the iTunes and iPod are up to date.