The pattern of symptoms does not fit, but your description of the sound reminds me of the buzzing sound we started hearing from the rear of our '04 330 about a year before the fuel pump failed. That noise was most apparent when the car was sitting still in the driveway idling. It came and went over a year and 10k miles and we never knew what it was until one evening the wife walked out of the grocery store and the car would not start.