I had the same thing happen to me on a Kenmore 90 Series Washer. The pump would pump out all the water, but the tub would not spin. The problem was the plastic transmission / motor coupler. The part was less than $10, but the washer will need to be taken apart. Cheap if you do it yourself (as I did), expensive if paying for labor. Hope this helps!
Mike Keller, May 2004