Looks like I typed that last entry too soon. While things worked okay last night, I got absolutely no signal this morning. After more cable wiggling, more detaching and reattaching, and more under-the-desk spelunking, I decided to try plugging my Mac laptop into the monitor. Bingo! Beautiful picture...and it was via the DVI input. After all the other tests, that could only mean one thing:
I've got a dead video card.
(BTW...absolutely meaningless bonus points for those who can decipher the slightly cryptic reference in this post's title. Think early 90's TV...)