When agitation stops and it is supposed to go into drain, do you hear any noise from the drain pump? If yes, then there must be a clog or the pump is failing. The washer must be drained before it can spin. If there is no noise from the pump then you need to check for 120vac at the pump wiring terminals. If you have power there, then you need to replace the pump. If no power, then looks like a bad timer. The lid switch is fine or else it would not agitate.

Eric