Took a longer look at this problem:
1) I uninstalled the USB hubs with Device Manager and allowed Windows to re-install them. Didn't work.
2) Booted the machine with a Linux LiveCD. It reported that there was NO communication with any USB ports.

My conclusion: motherboard is screwed. At least in so far as the USB hubs are concerned. This is not unexpected as the machine has always run at the upper end of the acceptable temperature range. It is still under warranty so I'll get the CStore to come down.

Problem: if the board gets RMA'd what do we do in the meantime?
Answer: Pull station 24 from Lab C and rebuild it as the TS.

UPDATE: I have a call in to the UVic CStore to come in and have a look.