Hello, Thank you for using this service, I will be helping you with your problem today
do you get water through the door ? does that work ?
the switch in the dispenser is good or the water wouldn't work, (same switch) your auger motor has failed. you need to replace it. its just below part # XXXXX on this diagram. part # XXXXX on this diagram. you can order this @ http://www.searspartsdirect.com/partsdirect/ part-number/Kenmore-elite-Parts/Refrigerator-Parts/2252130/0046/106/Model-10657712700/0583/0165000?keySuffixId=NA&pathTaken=partSearch&pathRender=modelComponen t&documentCompId=K0702004&diagramPageId=00006&productTypeId=x&searchModelNumber=10657712700&subCompDesc=Motor%20and%20ice%20container%20parts&brandDesc=KENMORE ELITE&modelDesc=SIDE-BY-SIDE-REFRIGERATOR&blt=11&shdMod=10657712700
the only thing I can do is send you the link to the diagrams. unfortunately you have to pry up on the cover once all the screws are out. it goes in through the top if theres no cover under. heres the link.
diagrams best I can do. thanks Bryan