Ice maker not filling and ice dispenser continually runs

I have a Kenmore side-by-side that has stopped making ice. When I first looked at it, the fingers in the ice maker were stuck, I took it out to see that the water level was also extremely low. After thawing a little bit of ice that got stuck where the shaft for the fingers spins, I now have that spinning.

Here is my problem:

1. The fingers that push ice from the ice maker into the tub will not stop spinning
2. The ice tray will not receive water.

What I have done so far:

1. Verified that water can run through the inlet tube
2. Replaced the water inlet valves

*Note: The water dispenser works and puts water out at a good pace.

Any thoughts?

Thanks!

***UPDATE: I did the live jump test and got the water to flow. So from what I have been reading, it may be that the unit has gone bad. I’m going to keep looking though.