Ice Maker Not Dispensing Ice?

I have Kenmore side by side. Two days ago everything worked fine and then it happened. It still makes ice cold water, but when I push for ice to come out nothing happens. I don't hear the motor or the crushed ice. What do I do? I have a nearly new refrigerator with ice in the door. The icemaker makes plenty of ice and when I hold a glass to the lever, a sound is made, but the ice only dispenses once in a while. After the first couple of times, we stopped trying and we scoop the ice out of the tray. The water dispenses fine. What could be the problem?