Washing machine will fill with water, but won't articulate
This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.
First, see the Sears parts site for your washer:
Enter your model number and you'll see a list of major sub-components with diagrams and parts.
I assume that you mean after filling, it won't begin the agitate cycle.
If you can hear the motor but the agitator won't move, it could be the "motor coupling". (See the motor section of the Sears site. This coupling is a fail safe between the motor and transmission. If the plastic prongs break, or the rubber center piece wears out, the transmission cannot agitate the washer.
If you can't hear the motor, it could be a timer problem.
Try to manually move the timer to a spin position and see if the motor / transmission move. If they do, it is most likely a timer.