@dilligaff F20 means that you have a water fill problem on the washer. " If the washer is not filling when the F20 appears:
Check to see if you have Flood Safe devices on the inlet water hoses to your washer. If you do, these devices could be causing your problem. They will activate to shut off the water flow to the washer at times. I do not recommend using these devices on this type of washer.
Turn off the water valves behind the washer. Disconnect the hoses where they attach to the back of the washer. Place the ends of the hoses in a bucket and check the water pressure and volume coming from the hoses. If the flow is inadequate, you will need a plumber to correct this fill problem.
When you replaced the inlet valve did you replace the small screen filters? It is ok to leave them out for a test as well.
If the washer is filling normally when the F20 appears:
Check for a siphon problem in your drain system. This could be caused by the drain hose being installed incorrectly. The drain system requirements for this model are illustrated in the second image below. Also, make sure that the opening at the top of the stand pipe is not taped shut. Air must be able to flow through this opening. The drain hose should not be pushed down this pipe more than 8".
Check for leaks in the hoses or under the washer. A leak can prevent the washer from filling properly. You could have a problem with the water level pressure switch, the flow meter or the central control unit (electronic control board). Also, an F20 on some models of Kenmore HE3t washers indicates a problem with the heater circuit. ". Let us know the exact model number for your washer.
See if you can run the diagnostic program for your washer and what code/error you get. Kenmore-HE3T-washer-techsheet.pdf