The first thing to try is charging the iPod using a different source - i.e. not the computer. Do you have a another USB power source that you could use?
Let me explain.
I've had a similar issue with my Classic this week.
When plugging in my iPod to the computer's USB, the computer chimed with the "device connected", but then chimed with the disconnect and the iPod showed OK to disconnect. iTunes failed to see the iPod. After trying this a few times (and re-booting the computer), I discovered that the iPod's battery had fully drained, even though it had been almost full when I first tried connecting it. It appeared that the connection to my computer had drained the battery and that it now had insufficient charge to work.
I resorted to putting the iPod on charge in a sound dock and waiting for it to fully charge. Once fully charged, I connected it to my computer in the usual way and iTunes recognised it straight away. A Sync then took place.