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I am assuming that when you hear the click the motor shuts off. This is the motor's internal thermal protect tripping as the motor is overheating.

Since the drum turns fairly easily by hand it sounds like you need a new motor.

I doubt it is the belt switch. if it was not being held closed by the belt the unit would never run.

Do you get heat when the motor is just buzzing?
Do you get heat when you manually start the unit?

The reason this is important is that the motor has two centrifugal switches on it. They close when the motor gets close to operating speed.
On of them switches in the heater. This ensures that the heater does not come on until there is air flow.
The other switches out the motor's start winding. If left in circuit this would overheat the motor.

So if there is heat when the motor buzzes it could be a problem with the mechanism that activates the switches re: they are always activated so the start winding is not in circuit. Could be just lint etc. May also need a motor replacement.

Do not let it run very long when it is buzzing. as if there is heat it will blow a thermal fuse.

If there is no heat when it buzzes but there is heat when you manually start it then I would replace the motor.

I am off to the lake later today so will not be available till next week.

That your motor starts if the drum / belt is pushed manually it might be the starting capacitor needs replacement. You can google "dryer motor starting capacitor" and see some detailed links about that.