I think I've figured it out. Yesterday when I went to turn my machine on it did the same thing as all the rest of the week, it just stopped at q-code 19. However, I couldn't get it to start by wiggling on anything that I wiggled before. Not the power cables, not the memory, not the graphic or sound cards, not the chipset heatsinks, not even the CPU heatsink. Then I remembered I still have a dual serial port PCI card in the system (note that I have the machine in a nook beside my desk and I can only blindly reach into the case and I'm too lazy to pull the whole thing out ;-) ). So I reached behind the graphics card and pressed down a bit on the PCI card. Voila! The machine booted. This morning it booted fine as well. All my previous wiggling must have flexed the board just enough to fix the seating of the PCI card temporarily.
I now recall I had a similar issue over a decade ago when I installed a new PCI card into a machine with a case that wasn't all that square with the expansion slots. It wouldn't boot or beep at all with the card in. I remember I had to loosen the holding screw a bit to let the card sit in the slot better and then it worked.
Next week I will continue to boot my machine every morning and see if the fix lasts. If I don't report back here then that was the problem.
Glitz.