That evening, I fired up the computer and it started perfectly. Not sure what the problem might be, I checked hardware settings, and shortly after double-clicking the C: drive, the machine froze with the message of "Not Responding" in the title bar of the C: drive. About 60 seconds later, the blue screen of death appeared, and the computer restarted itself, this time acting as it did for the student: declaring that it could not find a boot drive.
This didn't look good. I removed the side panel which had a fan mounted on it. The fan did not originally come with the case, but was added after the initial build, and utilized a regular sized molex power connector which was daisy chained to the boot drive. I tried bypassing the fan, connecting the power rail directly to the boot drive and turned the power on. The computer started up, and stayed running.
I checked out the pins in the molex connectors of the fan, and they were all pretty loose. The 5V+ pin in particular was pushed way back into the connector.
So it was the decorative fan that was the problem! It's a little funny as I look back now because the fan was purchased after the fact, specifically to help make the computer look cool. It definitely achieved that goal, but two years later ended up being a nuisance. The connection was not great from the start, but it was never noticed, because it wasn't a problem until the computer had to travel a few times in a car for it to become loose enough to cause the boot drive to not be powered correctly.
Looking back, It was probably not the best idea to purchase the least expensive fan that could be found on Amazon.com (this one was about $7.00 if I recall). Thankfully, this ended up being a fairly easy repair.