There is, now, a new wrinkle -- a happy but unexplained turn of events. I brought in the monitor to a SONY repair for a repair estimate. They came back with a figure well over $250. Way too expensive, so I didn't authorize the repair, and instead took the monitor back home. I downloaded a schematic, thinking I would at least give it a a try at puzzling out what was wrong (and thank you for your suggestion to begin by measuring the AC output).
But here's what happened: I plugged in the AC adapter. The monitor powered on! Curious. I tried the remote. It worked. I tapped the screen. The touchscreen functions are back - and perfectly calibrated. I can't figure out what happened. A by-product of the SONY technician fiddling around with it it come up with an estimate? A cosmic gift from all the good energy flowing from fixit? Gratitude from an older device for my loyalty to it? I'm puzzled, but happy.