Moments after I posted my original question, I decided to go for it. Here's what I did.
Grasp the remote in two hands with the "Light" button sticking up and closest to your left hand. If you rotate the top of your left hand away from your body and the top of your right hand towards your body, flexing the remote, a small opening will appear to the right of the "Light" button. Get a small screwdriver in there and start working it around the perimeter of the remote. There are indents every inch or two around the remote. Be careful when separating the shells as the battery holders are integrated into the black part of the shell and can bend easily.
Once I got inside, I found that the LCD panel had become completely disconnected. I just needed to plug back in the LCD panel ribbon cable and the remote worked perfectly again.
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