Hi, I have an Amana Electric Dryer that has a buzzing sound when I push button to turn on. Buzzes but won't turn on. Previous to this it would it turn on but shut off sometimes 5 minutes sometimes 20 mins. Now it just buzzes. Any ideas what this could be?

Here are your parts
Replacement parts for Amana LED20AW DRYER- ELE | AppliancePartsPros.com

Here is a manual that may be helpful.
http://appliancejunk.com/forums/index.php?action=downloads;sa=view;down=404
You may have to join the site to download the manual but it is free and has tons on info.

Try rotating your drum in the correct direction by hand. should turn fairly easily. You may want to try this on a couple other units just to get a feel for it.
You may have a mechanical problem with the drum mounting so it is putting too much drag on the motor.

When the unit shut itself off could you restart it right away or did you have to wait before it would re-start? If you had to wait then the motor is probably overheating. It then pops it's internal thermal protect and the motor then has to cool down for the protect to reset.

If it is hard to turn, run your fingers around the seal at the back and front of the drum to see if something is jammed in there. Be careful in case it is sharp.If nothing open the unit up and check the front glides, the rear support rollers, the idler wheel, for anything in the blower assembly, the motor etc.

Do you have heat when the motor is not rotating?
This would indicate a problem with the motor's centrifugal switch.
This switch is supposed to activate when the motor gets close to operating speed.
Part of it switches in the heating coil.
The other part switches out the start winding.
So if it is activated at rest then you do not have a start winding an motor will just buzz.
Could be it is just jammed solid with lint.

If it rotates OK.
This may take 2 people
Open the door
Manually hold the door switch closed
Push the start button and manually rotate the drum in the correct direction.
Watch your knuckles in case it starts up.
If it does start up, odds are high that you need a new motor.