Unfortunately, I don't think there is a 64-bit Windows version. If you know someone with an older Windows PC or any Mac, maybe they can run it for you. Or, if there is an Apple Store nearby, you can make a reservation at the Genius Bar and have them give it a try.
Does the shuffle still appear in device manager? If it does not, and it does not charge when connected, the problem is more likely to be with the USB connection. That would probably mean the USB cable/dock is bad, or the connector (headphone jack) on the shuffle has become faulty.
It could also be the USB port on the computer. If you have not already, I would try the following. Shut down (power off) the computer. Use this procedure to reset the iPod
Disconnect ALL USB peripherals from the computer, except for standard mouse and keyboard. Start up computer with shuffle NOT connected. Run iTunes. Connect shuffle to a direct USB port on the computer.