Whirlpool Ultimate Care II Washer Model#LSQ9665JQ4

sounds to me like the motor coupling is broken,this youtube video will show you how to replace it
http://youtu.be/9K1KHEogf3c

Could be a problem with the lid switch or motor coupling. Does it drain? Does it spin?
when its time to agitate or spin, do you hear the motor?
Lets start with the lid switch. open the lid and use a screw driver to push the switch down. pay attention to see if you hear it click. Try to run the unit with the screw driver holding down the switch.
Let me know what happens so I can further assist you.

If you have motor sounds after water fill,but no agitation or spin it could be a broken direct drive coupling. If it will not pump out water,there could be something stuck in the drain pump.

You have a bad motor. Your washer is a direct drive machine. It turns in one direction to agitate and the other direction to both spin and to pump. You have lost one direction in your motor.

your dog ears are bad.
You can replace them for about $10 @ your local appliance store.

Replace the direct drive coupling on the motor.

Thats very agitating.There is a motor that runs the agitater,its either going out or you have lost the drive,a little spendy to have fixed.
Hope this helped.Let me know by rating me
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lenwest

motor coupler is goingto be the issue, easy enough to replace, you can find a video on you tube, search "whirlpool motor coupling"

does it spin?
sounds like your coupling is broke.It takes the place of the belt if it breaks it won't spin or agitate. it will still pump though.
Part # 285753A

It sounds like the coupling between the motor and gearbox has worn out. It should cost around $15 plus shipping and handling.