I have two suggestions. There is an iPod Reset Utility
http://support.apple.com/kb/HT1238
that is only for the 1st and 2nd gen shuffle. It does something like a Restore in iTunes, but works at a "lower" level in cases when a Restore in iTunes does not work (or cannot be used). For it to work, the shuffle does need to be seen by the system, and it sounds like yours meets that requirement.
Unfortunately, I don't think it works with Windows 7. If you happen to have an older PC with 32-bit Windows, you can use that PC to run the utility on the shuffle. Or, maybe you have a friend with a Mac or 32-bit Windows PC that can run it for your. Or, if you have an Apple Store nearby, you can make a reservation at the Genius Bar and ask them to look at it and run the reset utility.
The second suggestion, if you don't have a convenient way to use the reset utility, is to use Windows to reformat the shuffle's storage like it was a flash drive. Use a "full" format (not the "quick" option). Use the "FAT" format type. Make sure iTunes is NOT running. After it is reformatted, it will be blank. When you run iTunes, it should recognize the shuffle and ask you to Restore it (to re-install the software and set it to default settings). Hopefully, it will work this time.