Whirlpool dishwasher doesn't start agitating right away

Hi: I have a strange problem with my '96 Whirlpool Quietpartner 980 dishwasher. At the beginning of each wash or rinse cycle, the tub is filled, and the pump should start pushing water up through the columns and through the arms causing them to spin. When this dishwasher was new, the "agitating" would begin before the timed fill cycle was even complete. Now, the agitating occurs from 30 seconds to a couple minutes after the tub has filled! If you open the door real quick to see what is going on in there while it is "trying" to start, you see that the water has been swirling around in the bottom of the tub, and a few air bubbles come up to the surface of the water. Here is the kicker.... If you then shut the door, the agitating starts IMMEDIATELY. In fact, this hack solution works all the time. All you have to do when it is "stuck", is just open and close the door for a second, and then is starts up immediately. When it is in the "stuck" state, the motor seems to be turning just fine. It doesn't sound strained at all. It seems to me that the impeller is cavitating.
OK, so I got the repair manual, and tore down the pump as far as I could from the top. (Actually, you can get quite a ways into it from the top!) There are a couple things that are suspicious to me. Unfortunately, the darn repair manual is a "tear down, put together" tutorial that doesn't explain what everything does. Anyway, there is a valve which consists of a plunger, spring, and rubber end, and also a check valve. These live in the donut shaped white plastic "torus" or "seperator" as Whirlpool calls it. I have no idea what these do. The manual is no help. They look fine. There is nothing obviously wrong, or no visible gunk anywhere. I suspect these because the problem seems to me like it could be caused by the pump getting stuck in this "cavitating" state, then when the door is opened and closed, the air bubbles go to the surface, and then when the thing is restarted, it takes right off. Maybe one of these vavles is sticking???
BTW, I also suspected that maybe the tub did not fill with enough water, but I tried prefilling with a couple extra gallons and this did not help. Also, this theory does not fit with the "open and shut the door" hack.
So, my first question is does anyone know what these things do? Second question would be if anyone knows what specifically would cause the problem?

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