This just keeps growing!
Figured I would answer your email here since you sent the same video to me earlier in the day.
First,you need to disconnect the pump power by disconnecting the black and white wires that come out of it. If you ever intend to use it, you don't want to keep cooking the windings and the start switch contacts.Remember, I told you that you can't buy that start switch anymore!
Second, your fill valve diaphragm is shot and that is why it is leaking.So make plans to rebuild or replace both of the valves as the second rinse valve will probably be just as bad.
Third,you photographed the supply valve for the booster a few days ago so you will need to turn that on to see if the water will run thru the booster and how well the second fill valve works.
The normal sequence is fill with valve 1 and wash pump runs, then drain solenoid opens(pump running at same time), then it closes and then valve 2 opens to partially fill and then drain snaps open again, then valve 2 opens to fill completely and then the drain solenoid opens again to drain it. The pump stops as the timer comes to the end of its cycle.
I told you that the timer has 2 complete cycles within 360 degrees of rotation. It will stop cycle 1 at 180. If you unlatch the door which you did at the end of the video, it will advance to start another cycle as seen in your clip. The machine doesn't care if the door is opened or not, it has a switch mounted at the latch to make the timer ready itself to start again as soon as the door is closed and latched.
The black stuff could be crap inside your building plumbing or the diaphragm as well. All you need is a piece of galvanized or black pipe somewhere in your water line that someone may have used in a pinch and you can get the black stuff coming out. But getting the machine working is the first priority.
In all honesty, Mike, you will probably have a much easier time pulling the machine out when you are really ready to tackle this project. You have too much stuff to fix in a very small area in which to work and it is much easier to be able to attack it from all four sides and to even turn it over if need be.(please remove the wash arm before turning it over)
You know how to reach me if you need to as well as anyone else here on the forum.
This should be enough to ponder for you for now!
Later
Steve