3. If still not working, carefully examine the SD card slot looking for any damage especially any that would result in one or more of the contacts between card and socket not being made.
I removed the Pi from its case and did all of the voltage checks, which passed with flying colo(u)rs. I burned a second SD card with an image which also did not boot, but as I plugged it in, I noticed a small sliver of plastic which fell from the SD card socket.
Sure enough: the SD card socket was damaged. When I held down the card on the contacts (not possible when it was in the case), the boot worked fine, even with the HDMI/DVI connector.
*TOTAL* wrong diagnosis on my part (facepalm).
Thanks for the tips. The NEXT question is what to do about a damaged SD card slot. Off to the forums.
THANKS for the tips! Now what next.