Model # KCMS1555RSS1
, this microwave would run and make the usual sounds when started, but it would not heat the food. After removing the cover I went to discharge the capacitor and found the problem. It appears the capacitor was breaking down internally and trying to shed it's skin. Not being able to hold a charge anymore (try and discharge it anyway) the high voltage section was not available to fire the magnetron, thus no heating. Replaced the high voltage capacitor and now the unit is cooking again just fine.
Just a quick disclaimer. If you take the cover off your microwave, unplug it and discharge the capacitor by placing the shaft of a screwdriver with an insulated handle across the two terminal lugs, and then touch each lug to the frame. You may or may not see a spark, but do it for good measure. Most electricity in appliances is only shocking. The high voltage section of a microwave can kill you.
KitchenAid Microwave High Voltage Capacitor Part # 8184813