Based upon troubleshooting recommendations I found online, I put the dishwasher into Consumer Error Mode by pressing and holding the Select Cycle and Start buttons for 5 seconds with the door closed. The LEDs on the control panel started flashing, which indicates the dishwasher thinks the door is open when it isn't. That points to a problem with the door switch or control board. The control board was the culprit in most of the online reports I found, and it appeared to be easier to replace than the switch, so I decided to try it first.
I ordered a WD21X24901 control board and replaced it using the procedures in this video:
http://www.anrdoezrs.net/links/8373913/type/dlg/https://www.repairclinic.com/Repair-Library/Part-Replacement/2091/Ge-Dishwasher-Main-Control-Board-Replacement-Wd21x20720
Note the video is for a slightly different model dishwasher, but the configurations were the same.
The control board was fairly easy to replace. I had a little difficulty disconnecting the electrical connectors on the control board, but just kept gently wiggling them until they came loose. After I replaced the control board I held my breath, pressed the start button, and the dishwasher started up!