You have one of two problems. If your machine sounds like it's trying to
agitate, you will have a bad coupler. If it just does nothing after it fills, your lid switch is bad.
For your lid switch, click on this
http://www.partselect.com/MultiModels.aspx?ModelNum=kaws850l&searchTerm=img_HWUP4CX3&RefineSearch=0&imgMfg=Whirlpool tha lid switch is #11.
Machine will not agitate without the lid closed and a bad switch makes the machine think that the lid is open.
For your coupler, click on this
http://www.partselect.com/MultiModels.aspx?ModelNum=kaws850l&searchTerm=&RefineSearch=0 the coupler is part #13 ( comes with all 3 pieces ) The coupler connects the motor shaft to the transmission. When bad, the motor will spin but the trasmission will not.
Note: Unit will pump water even with a bad coupler because the pump is connected directly to the other side of the motor shaft than the transmission.
Also, to replace the coupler or lid switch. Take the machine apart through the top. Remove screws from the front edge of the console click on this
http://www.partselect.com/MultiModels.aspx?ModelNum=kaws850l&searchTerm=&RefineSearch=0 Remove both #8's. and unplug the wire from the lid switch.
Then click on this,
http://www.partselect.com/MultiModels.aspx?ModelNum=kaws850l&searchTerm=&RefineSearch=0 and remove both #6's. Once you have removed the #6's, you will be able to pull the case foward just a little. Then you can unattach the hose connections. Once you have deattached everthing holding the case from pulling forword, tilt the case to you and lift off the bottom frame. Now you will be able to replace both the motor coupler and or the lid switch.
If I were you, If the coupler has never been replaced, or if you can see a black dust on the floor under the middle of the unit. I would go ahead and do so. The motor coupler is the most common part to fail on machines like yours. Under normal use they will fail anywhere from every 4 to 8 years. Less if you load it heavy, more if you load it light.
I hope this helps and Good luck