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Replacement parts for GE DS4500EB2WW | AppliancePartsPros.com

Did you check for a grounded element.
Unplug the unit
Remove both wires from the heating element.
Check it should be around 10 ohms.
Then check each heater connector to case/frame bothe should be open (infinite ohms)

Getting tech info on GE's is difficult, they like to keep it a secret and thereby keep their tech's busy.

It looks like your unit is a dual element type so both elements should be on in high temp cycles.

Here is a good site with dryer info
http://www.applianceaid.com/dryers.html
Take a look at #5 "GE" and ten #28 "Sample wiring" your unit may be close to one of these. The old unit shows how GE regulates the temp when they have a separate temp switch.
Check in the control console for the wiring diagram for this unit.

If you look at the wiring diagrams, you will see that the timer motor is connected through a resistor to one on the heating elements.
When this element turns off the voltage is applied to the timer motor.
The resistor reduces the voltage (240) down to 120 which is what the timer motor requires.

If this element is grounded or broken the timer never gets any voltage during Auto cycles so does not advance.

For timed dry the timer is connected through a different circuit path to half the line and so advances all the time.