I unplugged it and plugged it back in again, in a different USB port.  I rebooted the computer.  It would turn on and then, at one point while XP booted, it shut itself off.

I connected it to my laptop and it worked fine.

Too tired to mess with it anymore, I went to bed.

This morning I woke up knowing what to do.  Weird how that happens.  I went into the hardware manager and looked at the USB section.  Lo and behold, the USB drive was there, and it had been disabled.

Right-click, enable.  OK.  Fixed.  No problem.

But why did it happen in the first place?  Did the iTunes 8.2 install script need to disable other USB hard drives during the install, and then in a forgetful moment, neglect to re-enable it when it was done?

Anyway, if any of you are having the same problem, here’s a possible solution.