If you have to restart it by using the push to start, it sounds like the motor is overheating. The thermal cut-off is tripping and you have to wait for the motor to cool down for the cut-out to reset before you can restart.

Try rotating the drum by hand, it should turn fairly easily.
I know fairly easily is not a very good description so you may want to try this on a couple other dryers to get a feel for it.

If OK
Let it overheat and then open the door and try turning the drum. Just to check that perhaps once the drum heats up it starts to bind somewhere.

I am assuming that you gave the motor a good cleaning when you replaced the parts.

Could be you did not get the drum reinstalled quite right.

If you replaced the parts because this was the original symptom then the motor is probably toast.

FYI: The motor has 2 centrifugal switches. They close when the motor gets close to operating speed.
One connects power to the heater, this ensures that the heater cannot come on unless the motor is running re: has air flow
The other removes the motor's start winding from power so only the run winding is in circuit. If the start winding continues to get power while the motor is running, it will overheat.