Cool beans. Thanks, ZFR, now I know how to edit my registry! Watch me go.
Unfortunately, that doesn't appear to have been the problem: Apparently, the message I was getting before, and am still getting now,
Internal Failure
Error Number: 0x80040707
Description:
is about something
other than "You're not allowed to install this because it's already installed." Guess I'll have to actually take my computer in to the shop. And won't THAT be a joy.