Is it the motor humming or the timer? If motor, with it sitting on the floor, try spinning it by hand as fast as you can when it's humming. If it doesn't start, closely inspect the terminals at the motor connection for corrosion, burning or signs of overheating. Also inspect the connections at the timer. Can you provide an image of the wiring diagram? In most older Whirlpool models, the lid switch would only effect drain/spin mode but can't be sure without seeing the diagram.

Eric

Connector picture isn't very clear but even so, I can see the corrosion. I assume the contacts inside the motor switch receptacle are bright and shiney since this is a new motor. Why was the motor replaced? Did the machine work ok after replacing the motor? The corrosion can definitely cause this problem. The capacitor is only used for starting the motor. If the motor was getting full voltage via the blue and white wires, you should be able to start it manually. The pins can be removed from the plastic plug for possible cleaning depending how bad it is. I't also possible moisture has wicked up into the wire and damaged it. The problem can also be caused by bad contacts in the timer. At this point, you really need to take some voltage measurements at the motor connector while it's plugged in and humming.

Eric

Well, the difference between agitate and spin as far as the motor is concerned, is direction of rotation. This really has nothing to do with the motor itself as direction is determined by polarity of power applied to the start winding relative to run winding polarity, which is determined by the timer. If you have a multimeter, I can advise how to check voltages at the motor connector.

Eric

Try to be quick about taking these measurments, it's not good for the motor to leave it humming like that. During agitate or spin mode check for 120 volts AC across the blue and white wires as well as across the red and yellow wires. Anything between 110vac and 125vac is good.

Eric