I had to do two things: Replace the water inlet valve and remove the ice blocking the fill tube.
The replacement of the water valve was pretty easy. Just remove the screws and pull out the old valve. It took me a few hours of looking online to figure out that the old style of hose attachment (a threaded connector) was very easy to convert to the push-in style on the new valve. I was confused because the new valve looks very different and there was nothing to suggest that they are really compatible despite the difference. I wasted time looking for the exact same valve. Of course, the valve by itself didn't fix the whole problem. I had to melt the ice out of the fill tube inside the freezer.
That required removing the ice maker to get access to the fill tube. Then I used a hair dryer to heat the fill tube. The hair dryer was constantly battling the freezer air so it took a while. I could have used some tips on how to not melt the plastic side wall of the freezer. My tip: use a stack of towels to cover everything except what needs to be heated. The fill tube melting took about 20 minutes and towards the end, I was able to use nose pliers to pull out the last 3" piece of ice. It all is working well.