Hi and welcome to FixYa, I am Kelly
When everything but the heat works there are 2 common components that fail. The high voltge capacitor or the high voltage diode. In rare cases the magnetron fails because the oscillator in the top of the magnetron sticks. When the oscillator sticks the magnetron makes a LOUD humming sound and you do not get heat. However.... a open diode or shorted capacitor will make the exact same sound briefly before the main in line / internal fuse fails.
The capacitor and diode are items 4 and 9 this link:
http://www.appliancepartspros.com/partsearch/model.aspx?model_id=504310&diagram_id=28243249#d28243249
NOTE: Before doing ANY maintenence you must hold an plastic handle screwdriver back on the handle and ground the capacitor terminals at least 3 times. (Just in case it has not failed.)
Failure to do so will ruin your day and pass along one heck of a shock.
To check the diode you must disconnect one terminal first. The read it with a meter. Reverse the leads and check continuity again. It should read continuity in ONE direction / polarity only. Id should NOT read open both ways or shorted both ways.
To check the capacitor you have to remove all the terminals from ONE side of the capacitor terminals. With the meter on R X 10,000 probe the 2 terminals. You should see a brief jump in resistaqnce and then the meter drifts to infinty. Reverse the leads and do this again. You must get the same jump in resistance and then the meter drifts to infinity. If it does not do this it has failed and must be replaced.
If both the diode and the capacitor pass the checks above the next step is to check the magnetron for continuity across the 2 terminals. It must read continuity. Even if this test passes the oscillator can be stuck and it will not heat. (Again if it is stuck it will make a LOUD humming noise.) It is not repairable.
I suspect you either have a bad diode (most probable cause) or bad capacitor (2nd most probable cause).
Thanks for choosing FixYa,
Kelly