Windows Updates Fail: Register wups2.dll

Working on restoring a bunch of desktops to their pristine state I discovered that one of them could no longer install Windows updates.

It's an HP Compaq d530 SFF, although I'm not sure that the hardware had much to do with this problem. After restoring the HDD to the factory state using the original Windows XP SP2 CDs, and installing SP3, I discovered that every Windows update attempt failed.

Apparently there is a dll that needs to be registered and installing SP3 right after restoring the system can cause this.