REMEMBER TO ALWAYS UNPLUG AND SAFELY DISCHARGE THE CAPACITOR WHEN OPENING UP A MICROWAVE
I first had to open the microwave and run all the individual component troubleshooting tests listed in the repair manual (which required a multi-meter). Everything tested good, except I did not want to run the test which required measuring the voltage from the main board while it was running since it did not seem safe to me. However, I checked that the humming noise switched on and off when I ran the microwave at less than 100% power, which I believe checked a similar thing. Because this suggested that the control board was good, the manual suggested that I replace the magnetron in this case. Accessing the four screws on the magnetron was a bit annoying, because it required taking the whole plastic venting apparatus off on top of the microwave, but once I did that everything went smoothly and the food started heating again.