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Replacement parts for Whirlpool LTE6234DQ0 | AppliancePartsPros.com

See the attachment for a wiring diagram, closest I could find to yours was a DQ2.

When you say the timer does not advance in any setting do you mean in both auto and timed dry modes?
The timer motor gets power from different sources in each mode.
Timed Dry: 120 volts TM/OR timer contacts switch in Neutral to L1
Auto Modes: TM/OR timer contacts switch in L2 so motor gets power when the heater is shut off through the heating coil and the resistor (drops the voltage from 240 to 120 for the timer motor) to L1.

So if it works in timed dry but not auto it could be a power problem, the heater is blown or worst case scenario the centrifugal switch on the motor is either not closing or bad. Also a bad connection somewhere.

First I would check the power
Try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker.
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.
Do this with the heater off and on.
[COLOR="Red"]Be careful as 240 volts is lethal !!![/COLOR]