Product review (5 stars): Ice maker won't dispense cubes; this may be the problem.
If you ice makes won't turn on, there is a good chance this is the problem.  The micro switches mount in the upper left and right corners of this bracket on little studs that get fatigued after years.  Just pop the outer trim off the outside of the door and see if the upper left micro switch is solid.  If it wiggles, you will probably see one or both of the mounting studs are broken.  It takes less then 10 minutes to replace this.  You'll an expensive service call and the repairman probably won't have it with him (another visit required) Check the upper left corner in the pictures.  The black thing is the micro switch attached to a mount that attaches to the two 1/8" diameter studs on this bracket.  I have it pulled away from it's mounting position by about an inch.  The bracket is held in place by two 1/4" hex head screws.  Just unplug all the wires, take the two screws out and transfer the few things to the new bracket.  It's a good idea to take several pictures in case you have trouble remembering where things go.