Kenmore 431423 won't advance cycle, won't agitate

Check here...

https://www.repairclinic.com/RepairHelp/How-To-Fix-A-Washing-Machine/47-6-607241-/New/Kenmore-Washer-Won-T-Spin-Or-Agitate-417-43142200

Give their techs a call at their 800# before throwing parts at it.

Best to you.

the lid switch controls the spin cycle, pump probably has clogged

How old is this unit may I ask?

This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.

First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action

Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.

Some Kenmore washers have a two piece agitator. The lower section will rotate back and forth both ways.

The top section has "agitate Dogs" that allow it to rotate only one way (to keep the clothes moving downward.

If yours has a two piece agitator there shouldn't be a problem.

If it has a Mallory/Sole motor speed control module located on the bottom right rear area of the cabinet, chances are THIS is the problem. They never completely quit working, just certain functions end up not working anymore---like yours. Various suppliers exist for this part ranging from $90-$150. Surf the net to find the best deal. Use your Sears model number on the search. I got mine for $82. Sears wanted $144.

the agitator dogs are problably remove agitator cap remove bolt holding agitator in ..dogs are part #80040

It's not your exact model but does have some good information about the possible causes.
http://www.shopyourway.com/questions/1099421

If you need further help, reach me via phone at https://www.6ya.com/expert/sean_97e45db9c0ed1da4

sounds like may be in clutch see if you can help the tub start spinning when trying in spin setting...if trying to turn or turns some and stops most likey clutch slipping

If this is a 417 model your problem might be the pump itself. There is a pressure switch that detects whether or not there is any water left in the tub. If so, it will not go into high spin. Remove the lower panel and check the pump on the lower right side. See if there is any gunk or coins in there by removing the hoses attached to it. Have a flat pan or a bunch of towells ready to catch the remaining water from the tub. If the pump checks ok, the next move would be to check the motor controller itself.