Linderman,
Your advice was right on the mark! I took out the eSATA card, put the modem back in, uninstalled it (I had disabled it but hadn't thought to uninstall), put the eSATA card back in... Windows recognized it as new hardware and reinstalled the drivers, and bingo! Success!
Now I can backup my whole computer overnight. Thanks for making what seemed like such a complicated problem turn out to be so simple! (and saving my weekend)
