Will not fill with water. Replaced inlet valve, water level switch, and timer. What is next?

Hi mrfneed and welcome, did you check the screens on the inlet hoses? What about the tube that goes to the water level switch is it clear? Can you hear the switch work when you blow through it?

Keep going and you will replace all the parts, but you still may not fix it. A good $20.00 digital meter would have been cheaper and then you would only have to replace the bad part. You need to test it like parttime said. Your water level pressure switch is usually the cause of water level problems, and not just this switch but how it is hooked up. It has a plastic tube that connects to a fitting on the bottom of the tub and if it is stopped up, full of water, loose, or has a hole in it then the water level pressure switch will not work properly. Most of these switches have a large metal diaphragm case with the diaphragm on the inside. These is an adjustment screw on the back side away from where the plastic tube connects that can be adjusted to change when the switch is activated, but on yours there may not be an adjustment. I do not know if you can use a better type on your machine than the original. Here is one at $49.00 with the diaphragm: https://www.appliancezone.com/ShowProduct.aspx?ID=3055
Yours is listed here for $115.00: http://www.repairclinic.com/Shop-For-Parts/a11b6/Kenmore-Washing-Machine-Parts?n=4
The switch is tested with a meter by taking the end of the hose on the tub off and blowing in it while you test the terminals with an ohm meter to see if it is opening and closing the switch inside. The switch has one common and one terminal closed with no pressure and one terminal closed when pressure is on diaphragm. Here are some manuals to show you all you need to know: https://dl.dropboxusercontent.com/u/8010163/Understanding%20automatic%20washer.pdf
https://dl.dropboxusercontent.com/u/8010163/Whirlpool%20Washers.zip
https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropboxusercontent.com/u/8010163/How%20to%20Diagnose%20and%20Fix%20Everything%20Ele ctronic.pdf
https://dl.dropboxusercontent.com/u/8010163/Whirlpool%20Direct%20Drive%20Washer%20Repair%20Ser vice%20Manual.pdf On page 7 of this manual you will find an excellent diagram of a fill switch and instructions on how to test it. Even if your switch looks different, like yours, it is still tested the same way.