I recently experienced this with my DE408, which is your dryer with heat buttons to the right of the dial. The buzz you speak of is not the actual buzzer but another hum. It SOUNDS like the start switch in the motor is stuck or bad. DO NOT operate this machine like that. The motor is trying to start but the start switch is not engaging the start windings. Since the start switch is not engaging, the heater is coming on every time you start the timer, because it is wired through the start switch for a safety. That way when the motor stops (like for opening a door) and the switch returns to it's rest position, the heat is cut and the drum stops. Problem is since the switch is not returning, it's not engaging the start winding to start the motor but it is completing the heat circuit. The "Switch" I am referring to is a centrifugal switch inside the motor. You can remove the motor in the dryer and try and clean it out, maybe spray some WD-40 into the switch, but it's not easy to get at on the square motors. You *MAY* have to replace the motor or have it repaired. Either way it needs to be looked at and I would not continue to attempt to use it. I had an extra parts machine and a good clean motor.

Someone else here may chime in as well, but that was my experience and I just replaced the motor with an extra as I have 3 people in the house waiting on the dryer to be fixed.

As to the washer question, do you mean the sound changes based on water level or based on the amount of clothes in it? What kind of sound is it? Could be a number of things, possibly dampers? Need more info on that one.

PS if worse comes to worse I am 4 hours away, I may have some parts and be able to fix it.

-Tim