Kenmore Ultra Wash does not proceed through cycle.

My Kenmore Ultra Wash 665.1307 does not proceed through its cycle. I push the Start/Resume button. The machine drains whatever water is in the bottom of the tub. The machine adds a little water and stops. Nothing further happens. The green lights above the Start/Resume and the cycle buttons remain illuminated, but the machine does nothing further. The water level does not get anywhere near the bottom of the heating element. A couple of times I let the machine proceed. Afterward I found the soap packet on top of the flatware rack. Clearly the machine had dropped the soap packet out of the dispenser.

My first thought was that the water-inlet valve had failed again. I replaced it, but the dishwasher still does not work.

I have tried different cycles. The problem occurs in Normal and One-Hour. I have not tried in Pots-and-Pans.

The float valve moves freely up and down.

I tried resetting the machine by pressing repeatedly the “heated dry” and “cycle” buttons. Some webpages recommend do this routine twice with “heated dry” and “normal wash." I have to push the “cycle” button six times in order to get to “normal wash” twice. Doing so makes no difference.

I do not think that the door latch is at fault, because the machine does turn on and start the cycle. And the soap pod eventually pops out.

I do not suspect the heating element, because the inside of the machine is suitably warm.

The problem came on gradually. Over the last few weeks the machine was less and less effective in cleaning the dishes. And then one day it stopped washing altogether.

(At the top of this question I show the device as a Whirlpool Quiet Partner. My machine is NOT a Quiet Partner. But iFixit insists that I choose one of two dishwashers as my device. I chose Quiet Partner because it may be somewhat closer to my Ultra Wash than the other device offered by iFixit.)

Any advice? Thanks in advance.