Fills tub but does not cycle. Waters turns off when filled but does not go to next cycle. Turning the dial to various positions does not activate any action.

PE error relates to the fill level of the washing machine. The fill level sensor is a pressure operated device. There is a sealed air line that goes from the bottom of the tub to an air pressure sensor. As the tub fills, it compresses the air in this air pressure sensor. When the tub is filled to the level selected on the dial, the sensor stops the fill cycle.

This air line can be plugged or the sensor itself can be faulty. This air pressure sensor is usually located near the top of the tub just under the top cover. If you can locate it, disconnect the air line from the pressure sensor and blow through it - it may be blocked by lint and soap from several washing cycles. There may be a filter in this line to help prevent this blockage. But the filter may have become blocked itself.

http://www.appliancepartspros.com/parts-for-model-kenmore-11023032100.html

The fill switch is bad. That's the only "safety" on the washer that will shut the water off after reaching desired depth. To test it, run your machine on the various water levels. For example, start out on the low setting. If the water doesn't shut off after the tub is half full, then it's the fill switch inside the unit next to the tub.

Rather hard to understand your problem from the wording in the question but what I understand to be the case is that your tub fills up with water and overflows after the cycle is finished. Perhaps overnight water slowly fills the tub. This is due to the water inlet valve not shutting off all the way. The Inlet valve assembly needs to be replaced.

clean pump and spray arm holes and any filters...you may need a pump kit if you see damage in your pump

The part you refer to is called the timer - find it here www.repairclinic.com

Hi, After the first cycle, and after it drains/spins, does it start agitating when the next load of water is suppose to be filling?
Please let me know so I can assist you further. Sounds like the pressure hoe from the tub to the water level switch is plugged.

Thanks
Vic

Do you hear the ticking of the dial moving? if so it could be that the points aren't getting connection to cycle it threw the various cycles

Sounds like what you are describing is the timer on the dial is not activating the next cycle. Timers are usually the problem when the cycles do not complete there cycle

Does the machine start working normally after turning the wash cycle manually ?