For posterity: filling, draining, but not washing can be as simple as a loose connection. My dishwasher (KitchenAid KDTE104ESS4) had the same symptoms as the OP’s, so after some research, I bought a replacement diverter valve as the cheaper and more likely of the solutions. When that didn’t affect the behavior, I took apart the circulation pump. Seeing no obvious issues, I measured the voltage being delivered to the pump during the wash cycle: 53 volts mostly, with brief increases to 112. I measured 10 ohms of resistance across the motor connections. Not seeing anything obviously wrong, I then plugged the pump back in while the wash cycle was running, and as I was plugging it in, the motor started running. Some fiddling revealed that the connection between the wires and the motor was loose. Even though the plastic connector on the wires was firmly clicked into the receiver on the motor. After facepalming a bit, I worked at the connection to get it to stay put. Moral of the story: check all connections first!