Thanks for your reply.
The machine would fill to overflowing and would not agitate. The problem was intermittent. About 1 out of 7 or 8 times it would work fine but then it would go back to overflowing + no agitation.
As a result of my research I replaced the Water Inlet Valves and the Water Level Control pressure switch. I checked all electrical contacts and wiring harnesses in the Control Panel. All were OK.
The problem continued,
I then disconnected the Small Rubber Hose (lets call it the SRH, for Small Rubber Hose) which runs from the Water Level Control pressure switch down into the Air Dome ( I think the name of the part I asked about is called the Air Dome) on the side of the lower outer wash tub. I disconnected the SRH at the Air Dome, leaving the SRH connected to the Water Level Control pressure switch. I set the machine on Fill and when the water reached the desired level I then gently bleu into the SRH, the Water Level Control switch clicked, the water flow stopped, and the agitator started. I then clamped shut the SRH. When the agitator cycle was completed and the water started to drain, I then released the clamp on the SRH. On the rinse cycle when the water level once again reached a desirable level I again bleu into the SRH, the Water Level Pressure switch clicked, the water flow stopped, and the machine went into its proper rinse action after which the water once again began to drain and I again released the clamp on the SRH.
We have washed probably 20 wash loads using the above described labor and attention intensive method and everything works fine.
So, the only possible source of our problem is the part (the Air Dome?) which causes the pressure to build in the SRH to activate the Water Level Control switch.