The ice dispenser in the door of our refrigerator quit. No noise at all. Any thoughts of a likely cause? Would there be a fuse?

If the ice container isn't pushed in completely and properly, the auger to feed ice out the dispenser won't spin and no ice will drop out.

The door switch and/or auger motor could be bad.

We called a repair man. Found out that Whirlpools are known for breakage of a part involving of the flap that seals the outlet that the ice comes out of when not spitting out ice cubes. That part was broken. With that not working we were getting frost inside from humid air wandering in. It turns out that the broken part is somehow part of the mechanical linkage from the lever you push your glass against to the actual electrical switch.

Whirlpool ice maker fuses are usually a single blow part of the wiring harness, if the fuse blows you replace the harness. http://amzn.to/2lJjz1Q

If the fuse was blown the ice maker would be dead.

What kind of refer?

Have you looked at the off/on switch? Mine has a switch. If the ice maker isn't used for a while it tends to lock up from the cubes freezing together. The switch is so you can turn it off while you remove the unit and free the cubes. Mine has been left off afterwards a time or two.