Cycle Control Knob Gone Bad

The machine will fill and the knob will click through the other phases of the cycles, but nothing takes place (no agitation, rinsing etc). At the end of the perm press cycle only I can force the knob into a "sweet" spot and with great pressure hold the knob while the tub drains and spins. I would like to remove the knob for observation, any idea how to do this or would it be a waste of time? Time for a new washer?

As long as the washer is in good mechanical condition
I would repair it. Its hard to be 100% certain without
some electrical testing but based on the way you describe it,
the timer itself is likley the root of the problem. You wanted
to know how to get the knob off, heres a pic below.

You have a non-repairable Kingston timer, I usually find a burn terminal causing the problem and if the contact is bad in the timer= new timer time.