Morning - thanks for the info Jake - as it turned out, I'm too stubborn to wait for advice and I kept tinkering last night since I had some free time over the holidays.
The washer had been starting off washing, but wouldn't stop draining and move to rinse/spin out the load. If I shut it off and left it for awhile and then switched it to quick rinse or drain and spin, it would spin the water out of the clothes, but they weren't clean. It had been doing this for a couple of weeks. I didn't have time to look at it because of work, so I was looking at new washers and cringing at having to spend money to replace this machine. That said, I didn't think it was the control board since the washer was able to understand the difference between starting a wash cycle and the quick rinse/drain and spin cycle. It just seemed as though something wasn't allowing it to get to the next stage in the wash cycle.
Doing a search online, I read someone talking about the air dome and the tubing to the pressure sensor as related to filling/draining water and how lint and gunk can build up in the tube and cause a lack of pressure to the sensor, which could cause the machine to either keep filling, or to not stop draining - sounded similar to my problem! To start, I pulled the hose off the air dome side and blew into it to see if there were any blockages there - there didn't seem to be any in the hose, and I could hear the pressure sensor clicking on and off as I blew into the hose. In the air dome itself though, it was about half full of black lint! No water in it, just what looked like black crud! And....there's not way to pull that air dome off to clean it.
I got a small tube from off of a can of PB Blaster and poked it in there to see if I could clear any gunk out or move it around - it looked like I was moving something - I hoped for the best. But, when I started the washer back up, now the water wouldn't stop running into the tub - it would not stop filling and was almost right up to the top! Clearly I had
agitated something (pun intended!). I turned the cycle knob to drain/spin and at least it drained the tub out, but this was no good either.

But I felt like maybe I was on the right track since I had now reversed the original problem from draining to filling - but something still wasn't allowing the machine to move to the next stage of its cycle.
When I looked at the air dome after I drained the tub, I noticed that it was now
full of water - I probably jarred some lint/crud loose which was blocking the path in or out from the washer tub. I did some quick Youtube searching --- I didn't find a lot on this particular problem except for a guy who used a can of compressed air to spray into and clear out his air dome. I had an empty can of compressed air which didn't help (why was I hanging on to an empty can?

), so I needed to find something that would fit in that small hole on top of the air dome! I decided to use an old syringe that we used to give our kids medicine when they were small. I thought I'd see if I could use it to push some air into the air dome to clear some of the crud. While I couldn't get the head of the syringe right into the top of the air dome, I was able to make a connection, and I managed to push the excess water out of the air dome. This seemed positive. I then took a syringe full of white vinegar and injected it into the air dome to see if that might help loosen more crud. I left it for an hour. When I came back, I gave the air dome another shot of air with the syringe and then started a load of clothes. It ran through a full wash/soak/rinse/spin cycle! First time in a couple of weeks. Since it was wayyyy past my bedtime when this happened, I shot another syringe of vinegar into the air dome and went to bed happy.
My wife is running full loads this morning to see if it will continue to work - so far so good! My next step is to see if I can McGyver something that allows me to hook my air compressor to the air dome and (at a low psi) do a better job of blowing more of that crud out.
Again Jake, thanks for the quick response, but happy I'm not replacing the control board!! Hope my explanation helps some people too. Does anyone have a better suggestion on how to clear out that crud beyond what I'm doing? How would a repairman fix this?
Grant