The problem turned out to be a defective power supply module. I was able to find a new replacement for about $100 and R&R myself with no problems (three screws, one plug in connector).
It turns out Apple did have a three year extended warranty on that part for my machine as there were lots of failures from my series of iMacs. Unfortunately, the warranty was three years and mine was four years old.
The job was easy enough to avoid the high labor rates at Apple and other repair shops. And of course I did get the upgraded supply to avoid a repeat of that problem.
Frank Van Alstine