You could have a faulty motor, or possibly a faulty timer switch.
Unplug the dryer, reach inside and try to rotate the drum 1/4-1/2 turn.
Plug the dryer back in and push the start button and see if it starts to rotate.
Sometimes motors get dead zones in them and this will help rotate the motor out of the dead zone.
If this does not solve the problem then the thing I would check is the motor.
Again unplug your dryer from the electric. Remove the box on top of the dryer that contains the timer switch, start switch, etc.
Be real careful not to knock any wires loose off of the timer switch.
Remove the top of the dryer, then remove the front of the dryer to expose the drum and belt, remove the drum and belt to expose the idler arm with pulley and motor. Now is a good time to check the condition of the belt and the drum rollers also. I will suggest that you oil the drum rollers at the shaft with a good grade of machine oil such as 3 in One oil. This will save a problem of a squeaky roller in the future. If the drum rollers have flat spots on them they will have to be replaced.
Then check your motor.
Note: Make sure you note how the belt route is, this will come in handy when you go to put everything back together.
If the motor checks out ok, then I would think it is the timer switch, you will have to replace the timer switch as they are not repairable.
I will include a couple of websites that have parts and live chat assistance:
I hope this helps.