The water to your ice maker is controlled by a valve. The valve turns on, allows water to run to the ice maker, then shuts off. The run time is very short; not much more than 5-7 seconds to fill the tray.

The water enters the freezer compartment down a ramp/tube. The ramp tube should be free of ice as should the very end of the ice tray where the water pours into the ice tray.

I just replaced the water/ice actuated water valves to my ice maker. When I turned it back on, water wouldn't enter because the ice ramp/tube was frozen up. I used a hair dryer to thaw it out. Even though I thought all the ice was out of it, there was still a loose ice plug that came out when the water ran the first time. It was able to come out because it shrank (was partially melted) with the hair dryer.

The next couple times the water came on it ran all over the place, including out the ice dispenser on the front of the freezer, so the water was obviously not getting into the tray like it should. Many sites will then say it is the ice maker and you must replace it. Before you do that, check to see if the ice tray inlet end of the ice tray (where the water from the ramp/tube pours in) is free of ice. Mine was froze up so I had to take the hair dryer to that too. I actually removed the screws from the ice maker so I could make sure I thawed that end out and it was totally free.

Try thawing both of these areas out first and see what happens.

Good luck.