It could be a host of things, but not the "drain valve", it doesn't have
one.
It could be:
The motor
The motor switch
Something caught in the pump
The timer
The transmission
The wiring





wrote

This is a Kenmore Direct Drive Washer...

Worked fine until one morning I put a load in, turned it on, and it
started fine.

Later that morning, my wife went to put the load in the dryer and it
was still full of water. The cycle was done though.

After manually draining the tub, I tried to run it through another
cycle. It fills the tub and the knob goes through the whole cycle, but
nothing else happens... it doesn't even drain the water at the end of
the cycle. During the cycle, I do hear some humming coming from the
machine (as if the motor was trying to run maybe???).

Along with this, there is a distinct smell of burnt wires or something
burning.

I've opened up the machine and determined that it wasn't the coupler.

What could be the problem/next action to take?

Thanks,
Brian