My Kenmore Series 70 dryer will start sometimes. If I leave it alone for awhile it will start and run for a few minutes. If I start and stop it a few times in a row I can usually get it to start 3-5 times before it stops working. Usually before it stops working It will hum as I hold the start button then that sound stops and i have to give it some time befor I can do this all again. I believe this means the moters bad. I’ve tested the start switch with a multimeter , door switch and what I believe to be is the thermal fuse, and they all seam ok.
If this is a gas dryer, check out the gas components, otherwise it sounds like a motor failure.