Ouch, sorry to hear all you guys having problems! For people experiencing this on only one computer I would of course try to uninstall Connect completely, delete all the remaining folders and then reinstall it, then hard reset the Reader and finally if nothing else works update your USB drivers.
Phebe, this is happening on two computers for you so it's probably a Reader problem, but a hard reset did nothing.
Do you happen to have a memory stick/SD card in your Reader? What if you take it out and then connect it? How long have you let it sit connected to your computer waiting for it?