This weekend we noticed our Kenmore (series 90) electric dryer was had an extreme burning smell and smoke coming from it. We turned it off and I opened it up later to find the bottom packed full of lint that obviously had been burning. I took it apart and thoroughly cleaned the entire thing. Put it all back together and when I push start it spins with a buzzing sound for about 15 seconds, then shuts off and it won’t restart immediately. After waiting 30 to 60 seconds their is a little click sound and it will start again, with the same buzzing and shut off pattern.
I called a parts store and they suspected it was the motor, so I picked one up and replaced it and the belt. Got the dryer all back together and still the same problem. I can’t figure out what the problem is and I’m down $135 for the motor to boot. 
I got up close to the under side during one of these cycles and I think the click sound is coming from the heater coil chamber, but I’m not totally sure.
The dryer is a Kenmore 90 Series Dryer (model: 110.60912990)
Any ideas?