In reference to your Kenmore Elite Refrigerator, Model # 106.56703500
Possible Causes for the dispenser not to work
Filter is clogged
No water to refrigerator
Dispenser is locked
If none of these possible causes are the problem, your chute may be clogged with ice.
Models with crushed ice,should have a couple cubes after dispensing crushed, to help clear the chute. See owner's manual for specific care instructions since ice buildup in chute is normal over time and will have to be removed manually. Do not use anything sharp to remove the ice as this may damage the ice chute. Use only a wooden spoon or plastic utensil to remove ice from the ice chute. If lever / pad is still being held after glass is full, ice will be forced back up the chute (no other place it can go). See owner's manual for correct usage instructions. Make sure to avoid setting the freezer too cold since "sub-zero" freezer temps can cause the dispensed ice to rapidly freeze to the inside of the chute causing an ice jam.
: On models that have the ice bucket mounted on the door, ice jams can stall and damage the dispenser motor.
TIP: When a large amount of ice is needed, e.g. filling a cooler, remove the ice bucket and dump the ice into cooler "by hand" to prevent overheating dispenser motor