Thanks for the ideas. Apparently some additional context may be helpful.
(1) Yesterday, my Mac Pro booted normally, but soon the monitor went blank. I had to hold down the computer's on button to force the computer to turn off.
(2) In a few minutes, I tried restarting. Still the monitor's screen was black. In fact, the monitor remained in standby mode. Further, when I tried my second monitor, it also remained in standby mode.
(3) Today, however, the computer booted and worked fine. Nonetheless, it seemed reasonable to run a test on the hardware.
(4) Every month, I run both Apple Disc Utility and Disc Warrior on all drives. Further both programs say all four internal drives are fine.
(5) No peripherals are connected other than the monitor, keyboard, and mouse.
(6) Neither my original Leopard OS package nor my original Snow Leopard OS package came with a second optical disc. Neither of the original OS discs will run Apple Hardware Test on restart with the "d" key depressed.
(7) I suppose that if I never can get Apple Hardware Test to run, and I have trouble with video again, I'll try booting from Snow Leopard (my previous OS).
I hope the preceding helps. Thanks again.
Jim