Is the piece of junk your computer or the iPod? Because the iPod works on other computers.
Have you read this article:
http://docs.info.apple.com/article.html?artnum=305136 Even if now new drivers are available, reload your USB driver in accordance with the instructions here.
After that connect your Shuffle to a rear port on your computer, disconnect all other USB devices other than your keyboard and mouse, and see if you can see it in Device Manager. If you can, change the drive letter to something higher, like M, and reformat the Shuffle (FAT32), not a quick format.
Now run the Reset utility on it.
Incidentally, how did your previous Shuffle have a disk problem when they don't have disks?