Diagnosis
The magnetron has failed. This is the high-voltage component that generates microwaves. A humming noise with no heat confirms it.
How to Fix It
You must replace the magnetron. Part number is WB27X20471. Disconnect power. Remove the outer case. Discharge the high-voltage capacitor (short its terminals with an insulated screwdriver). Unbolt the old magnetron, disconnect its wires, and install the new one.
If That Didn't Work
If the new magnetron still doesn't heat, the high-voltage diode or capacitor is also bad. Test them with a multimeter. Diode is WB27X20445. Capacitor is WB27X20446.
Heads Up
The capacitor holds a lethal charge even when unplugged. You must discharge it. If you're not comfortable with high-voltage components, call a technician.