Here are your parts
Replacement parts for MAYTAG MDE308DAYW DRYER- ELE | AppliancePartsPros.comSee the attachment for the tech sheet/wiring diagram
Here is the manual that comes up for that unit. Though it seems to mostly cover units with an electronic control perhaps it will be of some use to you.
16026315 Maytag Amana Dryer Repair Service Manual - ApplianceDigest.comYou have to join the site to download the manual but it is free and this is a very good site for manuals and other info for the appliance repair DIYer.
The light comes on and the door switch is good.
How do you know the switch is good?
Did you check it with a meter?
Just because the light comes on does not mean that the other side of the switch (normally open) is closing.
Also on this unit the light uses the L2 side of the power while the motor uses the L1 side so I would start by checking the power.
Try flipping the breaker off/on slowly a couple times.
Sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
Be careful as 240 volts is lethal !!!
Next I would unplug the unit and check the door switch, the thermal fuse and the push-to-start switch using a meter and ohms.