The dryer turns on with the timer control but will not automatically shut off. No matter what cycle you set the dial to, the dial never moves and does not shut off. You can manually turn the dial to off and it will shut off. I just replaced the timer control and nothing has changed even with the new part installed. The dryer heats, shuts off if you open the door, and all else appears to to functioning, but the dial never moves.

Here are your parts includes a wiring diagram
Wiring information replacement parts for MAYTAG MDE4000AYW DRYER- ELE | AppliancePartsPros.com

By "timer control", I am assuming you mean the Dryness Control Board.
I am also assuming that you have tried both timed dry and auto cycles.

Only way to be sure is to measure the voltage across the timer motor. If you get 120 volts and the timer does not advance then it is toast.
[COLOR="Red"]Be careful there is 240 volts at the timer and this is lethal!!![/COLOR]

Unplug the unit, place it mid scale timed dry and check if contact set 2 is closed.
If not then the timer is toast.
If there is no 120 volts in timed dry and timer contacts 2 are closed, then odds are that the replacement board is defective.

Contact set 2 that supplies power to the Dry Control board should be yellow and orange according to the wiring diagram.

Also always disconnect one side of any device/contact set when measuring for continuity/resistance. this prevents you from reading an alternate/parallel circuit path.