Turns out that the first one had a corrupted WMI service, with the rights for it way out of whack. How it got this way, I'll never know, but I at least had figured that out and fixed it by 10pm.
This other one though, has not been so nice. It's now 3am, and I still have yet to figure the source of the problem out. The install goes beautifully, right up until the installer tries to start the sqlexpress service, and then it just hangs. If I let it sit for about 20 minutes it will finally time out and state that it failed to start. The install then fails and I am back to scratching my head. As I write this, I am waiting on that timeout again; seems that the latest attempt to fix the issue didn't do any better than the last few. Unfortunately, the student will need the system first thing in the morning, or I'd set it aside and go home and sleep for a while.
I'll be the first to admit that late nights are just in the cards for IT folk, but it still doesn't make these nights any less annoying. Ever just have one of those nights where nothing seems to fix the problem, and the hours are slipping by unnoticed? Take some time and share, after all misery loves company.