Washing machine is Kenmore mod. 110 22422100. After setting load size and time setting I pull the dial and sometimes(most of the time) water won't fill and the agitator will agitate. What is the problem and hopefully solution

You have a broken point inside the timer. I hate to say that there is no cheap solution. You will have to replace the timer. There is no rebuild kit or anything like that to repair the timer. I know of two suppliers where you can buy a replacement. I use these sometimes when I regular supplier hasn't got a part in stock. I checked the price at both for you and found the best price at www.appliancepartspro.com . their cost if $123.08 plus shipping. They ship same day if before 4:ooPM. Their Part Number: AP3020181 . When you go to their site enter either your model number or this part number. If you enter you model #, scroll down until you find the timer, Th part # will take you straight to it. I sure hope this helps.
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I have kenmore mod. 11023542100 d/d washer . It is knot spin on but pump is spining