Putting in a graphics card in Martin's machine resulted in what appears to be a dead mobo (see Martin's post).
I set up Turnip as his workstation until we get things sorted out.

Here's the way things look:
The machine will make a regular POST sound; there is a brief flicker of light from the keyboard; drives and fans spin; mobo power indicator is on, etc. ad nauseum.

Going through dozens of forum posts, it turn out that this is not as strange as I expected. Lots of people complaining of similar (but not identical) problems. I've gone through every "fix" I could find with no joy. I've tested the machine with only one stick of RAM in each bank's first slot. I've tried with no HDD/DVD. I have not reseated the CPU (and I won't).

Tomorrow I will take it to the CStore and ask to get the board RMA'd.