I'm breathing a sigh of relief at having finally figured out what was wrong with Laila's computer last night. At 2 AM, I was finally able to translate the 1 long - 8 short beeps from the AMI BIOS into the appropriate "bad graphics card" message. In this case, "rad graphics card" would've been more appropriate--the Matrox G200 AGP just wasn't quite seated correctly.
It isn't like I hadn't already checked the card a few times, even swapping the previous card--with its feeble PCI bus--back in. Unfortunately, the motherboard was seated just slightly low in the case, causing me some difficulty with all the cards. Being more than a little bit frustrated and tired when I finally came to that revelation, rather than disassembling the box again (I'd already had to cannibalize my FreeBSD box temporarily for testing parts), I just hammered on the card until the motherboard decided that it was statisfactorilly seated. Heh. I'm pretty sure that moving the cable that I had had running under the end of Matrox probably helped a bit too.