Here is the parts breakdown
Replacement parts for WHIRLPOOL RED4440SQ0 29"electric Dryer | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208528190.pdf

I am assuming that in timed dry the unit's timer operates correctly.
In timed dry the timer gets power directly from the line.
In auto it gets power from the heating coil when it is turned off.
The timer motor is 240 volts so if it does not run in any mode, odds are you have a power problem.

First try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker and the heating coil requires the full 240 volts.
If this does nothing.
Measure 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 unit's terminal strip to ensure they are properly connected and none of them have burned off
If OK
Plug the unit in and check the voltage at the terminal strip. This is just in case you have a bad line cord. Be careful 240 volts is lethal.
If OK
Unplug the unit and check the heating coil and thermostats etc. for continuity.
Heating coil, should be 12 ohms approximately.
Thermostats and thermal fuse all should be 0 ohms.

The thermal cutoff (fuse) for the heater is Item 9 in Section 3.
If blown get back to us as there are other things to check in order to find out why it blew.

Be sure to disconnect one side of and device you are measuring this prevents reading an alternate/parallel circuit path. Also use your most sensitive ohms scale.
There is a good Sticky at the beginning of this forum on meter usage.