Hint: "Having" to wipe the HDD is not the sign of a "hopelessly broken" application.
Were you there?
I managed to clean the machine off so that it was at least usable. Then when I attempted to update the XP box to the latest update, I would get BSODs, every time.
So I would install what I could, until the BSODs wouldn’t let me install anything anymore. This was all in safe mode.
So I did some digging, and the corrupted FF install was preventing the update. Bad FF plugins that were infected.
So I had to wipe the machine and now it works fine, but she doesn’t use FF anymore. No problems since.