My whirlpool gold washer will not agitate. The washer fills with water but does not agitate and drain.

It is definitely not the lid switch because the motor runs but doesn't agitate and spin but it drains. This is rather a clear manifestation of a broken motor coupler. The mechanical output of the motor is not transferred to the transmission and therefore result in the agitator not to agitate and the drum not to spin. It drains because the drain pump is directly coupled to the rear of the motor shaft.

Remove the console from the top of the washer then flip to the rear and disconnect the lid switch wiring harness connector from the body of the washer.

The cabinet is attached to the rear of the washer by two brass-colored retaining clips. Insert the blade of a flat-bladed screwdriver into the lip of the clip on the cabinet side then push the handle rearward to release the clips.

Once the clips are released, open the lid and and grab the front rim of the cabinet then rock the cabinet forward and move it away from the machine.

I assume you mean the washer motor will not run in any of the drain and spin cycles. There is a safety lid switch located under the top which will prevent the motor from operating if the lid is opened or if the lid switch fails. If you listen carefully while raising and lowering the lid you should hear a faint click when the lid switch makes and breaks contact. If you do not hear the faint click, replace the lid switch.NOTE: Disconnect the power cord from the power source before placing the control panel in the service position. See image below
In order to access the lid switch, the washer cabinet will have to be removed. In order to remove the cabinet the console must be put into the service position. Remove two screws securing the control panel to the top. There should be a screw located at the bottom of each control panel end cap. Slide the control panel towards the front of the washer about 1/4 inch and then lift and hinge it over the rear panel. Disconnect the 3 wire lid switch harness plug from the top. Pop the two (2) gold colored cabinet clips off and tilt the cabinet forwards and walk it away from the washer. Remove the two (2) screws securing the lid switch cabinet and reverse the procedure to reinstall. Lid Switch part#3949247.

Helpful attachments:
I assume you mean the washer motor will not run in any of the drain and spin cycles. There is a safety lid switch located under the top which will prevent the motor from operating if the lid is opened or if the lid switch fails. If you listen carefully while raising and lowering the lid you should hear a faint click when the lid switch makes and breaks contact. If you do not hear the faint click, replace the lid switch. _NOTE: Disconnect the power cord from the power source before placing the control panel in the service position._ See image below In order to access the lid switch, the washer cabinet will have to be removed. In order to remove the cabinet the console must be put into the service position. Remove two screws securing the control panel to the top. There should be a screw located at the bottom of each control panel end cap. Slide the control panel towards the front of the washer about 1/4 inch and then lift and hinge it over the rear panel. Disconnect the 3 wire lid switch harness plug from the top. Pop the two (2) gold colored cabinet clips off and tilt the cabinet forwards and walk it away from the washer. Remove the two (2) screws securing the lid switch cabinet and reverse the procedure to reinstall. Lid Switch part#3949247.