As old as this thread is, some people are still posting to it. This is just a followup to end this thread on a completed note.
A few weeks after the initial problem I posted about, the problem happened again. In the end, I ended up declaring it dead.
When running the system (no video, again), I noticed it was getting VERY warm near the top of the keyboard, off to the left. I shut it down and dismantled it to find the cause, keeping in mind where I was looking. It looked like a couple components on the board, covered by the heatsink, were causing this. When I tried to remove the heatsink, I noticed a crack in the solder holding one of the components to the board. I'm not generally rough with these things and while old thermal compound can work almost like epoxy, I've never managed to break a solder joint removing a heatsink before. The other, identical, component next to it was undamaged and didn't budge under pressure.
My diagnosis is that this was a video component that had failed, or was failing, and the heat it was producing weakened the solder. I'm not as knowledgeable about core electronics as the components they comprise, so I don't know what that component was specifically, but it was obviously a core piece of the display system.
The heatsink and fan worked fine, as I'd cleaned them out already, so I think the heat was the result, not the ...