I have been working on this problem since 4pm yesterday; it is now 10:30am, I haven't slept, and I'm fairly confident that I found the answer.
Her machine was acting strangely and slowly...
So what do I do, but go over to Windows Update and see if I can install a patch.
I saw Windows 7 Service Pack 1 (SP1) had not been installed yet, so the genius that I am I chose to install it.
Boy was that a bad idea.
The machine wouldn't boot; it got caught with some Fatal Errors failing to install some patch.
I tried rebooting to a recovery partition. I tried running the standard Restore tools; they did not work. I tried 'sfc /scannow', and it said it couldn't fix everything. Obviously I also did not have a good Restore Point to go back to.
Rebooting, I got either "Fatal Error C0000034", or some other Fatal Error number, or the machine would simply stall at the "Starting Windows" screen and then go black after about 20 minutes.
This was so frustrating...
Eventually I must have found the magic search terms.
After booting with a Linux LiveUSB and backing up the whole drive to a server, I finally found THIS:
It involves what is basically a System Restore of registry entries back to the very original state.
Somehow, this "just worked"! The machine booted, it's happy (so far) and all of the programs and data are intact (so far).
I still don't really understand how it fixed things without breaking other things...
...and I'll be damned if I try going back to Windows Update any time soon; my wife is graduating at the end of this semester and needs a working laptop during that time.
So maybe in June or July we will find our install discs and reinstall from scratch just in case. But for now, so far so good.
If there is any other detail (or failure) that I need to add, I will post it in the comments. Please read.
I hope that people of the future get some use out of this post. Please comment if you found your solution here.
I leave you with the wisdom of XKCD: