There are these switches inside the microwave next to the control panel that detect whether the door is open or closed.
These switches had been burnt out, most likely because members of our household were apt to open the microwave door before the cycle was finished.
It was pretty easy to replace these switches - I watched a YouTube video on repairing a GE microwave, so I knew what screws needed to come out to get access to the switches. It was a total of 4 screws initially.
I snapped the old switches out and the new switches in. I put back the control panel and the vent cover. I had to take a 5th screw out to move a part over the control panel so I could snap the control panel back in.
And the microwave works! So worth it!