I have a Kenmore Elite King size top load washer. The washer will fill with water and just sit there. It will not start wash cycle. I will hear a click then a hum then nothing and about 30 sec later will repeat the same process. I can manually advance the timer to the spin cycle and unit will drain and spin but just will not wash. Could this be the timer or the motor switch. I assumed motor is good because it will spin. Motor does get pretty hot.
I would check the timer, probably bad contacts.
I have replaced the transmission, motor, coupler, lid switch and the machine still does the same thing. The timer is signaling the motor to agitate but the motor just hums. Could something in the pump allow it to turn clockwise but not counter clockwise.
Does the motor stop humming for a long period when it hums, if not, you have a bad timer and no pump clog. To confirm, remove the pump and re-try.