I updated the firmware, rebooted, and burned a perfect CD (one of my Maxells). So, once again, I am cautiously optimistic. I'll burn more CDs in the next couple of days and see if I stay lucky.
If not, I'll update
Nero (I got the full retail version of 6, and I'm at 6.6.0.14 now) and/or try hooking up the burner to my laptop (I can't believe I didn't think of that!). I attach the burner via Firewire to my desktop PC -- haven't tried it via USB yet. I've read a lot of arguments about which is better -- FW or USB -- but I don't know which is supposed to be the clear winner. (I'm not concerned about speed, only about burning successful disks). FWIW, I've got the old FW 400, not the new faster one.
Anyway, it would be very easy to hook up the burner to the laptop, so I can try that next if I get another burn failure.