Solved, after much gnashing of teeth:
1.) Uninstalled all Naturalpoint software, both the TrackIR and the USB drivers.
2.) Unplugged the device.
3.) Per instructions, rebooted PC twice.
4.) Re-installed the TrackIR 5 software.
5.) Plugged the device back in.
6.) Used the "run" box to fire up "hdwwiz.exe". In the Wizard, manually selected "Naturalpoint device" and then "TrackIR 5". Re-re-installed drivers.
And yes, I still hate USB.