Here are your parts includes a wiring diagram.
Replacement parts for MAYTAG MDE7400AYW DRYER- ELE | AppliancePartsPros.com

From your post I am assuming that it will not advance in timed dry or auto modes.

In order to troubleshoot this effectively you will need a meter.
Also very helpful having some experience working with electricity.

Put the unit in a mid scale run mode and check the power to the timer motor.
It should be 120 volts.
If there is voltage and the timer does not advance then the timer is toast.

If there is no voltage then odds are that the dryness control board is toast.

Be very careful when measuring and doing a live test.
[COLOR="Red"]
The timer has 240 volts at it which is lethal !!![/COLOR]

Often when it will not shut off in auto mode it is just a dirty moisture sensor (Item 6 in Section 7).

The sensor is just two metal strips with a space between them, a voltage is applied to the strips. When the clothes are wet the moisture between the strips gives a circuit path between the strips and a small current flows. The board monitors this and holds the timer off. When the moisture is gone the current stops and the board advances the timer. Any dirt etc. between the strips fools the unit into thinking the clothes are still wet. Usually cleaning between the strips with a damp cloth and drying it will solve a no advance in auto problem. Sometimes you have to clean it using isopropyl alcohol or electronics cleaner, you just have to be sure that all the solvent vapors have dissipated before trying it as the vapors are flammable.

It should not effect the timed dry.
I just added it as you said the wet light was on all the time so it points to there being a problem on the board.

Your problem is likely in the timer or the dryness sensor board.

The first thing to check is if the timer motor is getting 120 volts and not advancing then you know it is a timer problem.

Here is a manual which may help.
16023110 Maytag Sloped Front Dryer Repair Service Manual - ApplianceDigest.com