** only 3 things that are likely to cause this: a bad magnetron, a bad capacitor or a bad power diode. Can anyone give me some hints on how to decide which is the culprit? **
You can find test procedures for many microwave oven parts at the site at the following link. My guess by the sound would be a bad diode which often fries when it fails so there should usually be visible indications of a problem with it.