[used treasures]

If dryer is pluged in Heating element wants to cycle on and off with door open and dryer not running.

[denman]

Here are your parts
Parts for Kenmore Dryer 11068322700 - AppliancePartsPros.com

Sounds like the heater element is grounded.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run all the time.

Note the timer should not be at off, if it also cycles when the timer is at the off position you have more than one problem.