I fixed the problem!!!!!!!
From other, older posts by people with similar washer problems, I
learned that the washer will not spin as long as it has water in the
tub. This prevents the motor from burning out and/or water being spun
all over the laundry room.
After I finally figured out how to read the timer contact matrix in
the schematics, I checked all the timer outputs with an ohm meter and
they were correct. Since my major problem was the machine not
draining the water, I started following the DRAIN gray wire output
from the timer. Lo and behold, the gray wire went through the lid
switch before running down to the water pump or discharge solenoid.
One of the first things I'd tried when this problem occured was
pushing the lid switch with a screwdriver. It made no difference, so
I assumed the switch was good. However, when I actually ohmed out the
leads going to the switch, I discovered it was always open. Seems
that the contacts inside the switch are completely shot, to the point
that even operating it with a screwdriver won't cause them to make.
I've disconnected the leads going to the lid switch and jumpered them
together. This in effect sends the voltage for draining the tub
straight down below instead of routing it through the lid switch
first. The machine works fine now. Eventually I'll get around to
buying a new switch. Or not.