Well, I had my Intel iMac to the Apple repair shop here in San Jose, Costa Rica today. They explained that some (or maybe all) Input/Output functions are controlled by a dedicated chip on the iMac's motherboard. Sometimes that chip needs to be reset.
Here's how:
First, from the Apple icon in the upper left corner, click on Shut Down.
Then disconnect the power cord from the rear of the iMac.
Then press the power button on the left (as you're facing the iMac) lower corner on the rear of the iMac and hold it in for ten seconds.
Then leave the iMac alone for ten minutes or longer (presumably to let all the capacitors discharge, but what do I know?)
Then reconnect the power cord and press the power button on the back to restart the iMac.
They did this for me and tested it extensively. It seems to have worked!
(This seems to be consistent with the previous poster's experience of having the motherboard, and presumably the misbehaving chip, replaced.)