Kenmore Elite Dryer does want to start a cycle

I have a Kenmore Elite electric dryer that will not start the cycle when the start button is pushed. I push the button and it will spin a few times and then shuts off, might run for a second or two. I have to keep pushing the start button and it will finally kickin and run the cycle. I do not have a heating element problem, because the clothes do get hot and dry. I also dont think I have a thermostat problem since once it does start then the clothes dry. The dryer has been taken completely apart and cleaned of all lint, inside and out. The belt has been checked and the tensioner seems to be in the correct location because the cut-off switch is not engaged. Everything has been put back together correctly and the problem is still there. The motor also spin freely, when the belt is taken off or when you manually spin the drum with the belt attached.

I dont want to just start throwing $100 dollar parts at this thing, hence asking the professionals on the forum for help.

Thanks in advance.

Any help that can pe provided is greatly appreciated.

I went to an applicance parts store today to buy a new relay and start switch and the guy almost refused to sell those parts to me based on what I told him. The guy told me it was probably the motor.