Ok, here's another update.
I got hold of a Samsung 206BW monitor. Pretty nearly identical, just 1 inch smaller. All of the cabling and connectors are identical between the two monitors, so I swapped the entire electronics box (power supply and processor board) from the 206BW to my ailing 216BW. The 216BW continued to display exactly the same defective, scrambled display. So this rules out problems with the power and the processor boards. That leaves the LCD control board (mounted on the top, back of the LCD panel) and the LCD panel itself.
Well, further playing with it powered-up, I find that squeezing the LCD panel in a couple of spots on the edges results in restoring a normal screen image. So it is indeed the LCD panel itself (the thin film ribbon cable connections on the panel) that is having connection problems. :-(
Thanks for all the assistance. It was indeed a learning experience.