Looking in the parts breakdown for our freezer, I saw there was a single module for control and display. Others reported similar symptoms fixed by replacing the module, so I ordered one overnight (the freezer was thawing).
There were no instructions in the box, but the online part description indicated it pries out and pops back in. That was just the way it was: I turned the power off to the freezer, pried the control out with a putty knife and a screwdriver, then pushed the Control Display replacement in. When I turned the power back on, it all worked like new. It took about five minutes, including the "stare and compare" to be sure I had the right part.