So we went to another place. Their Laptop expert came out. He hadn't ever worked on one of those before. Wasn't sure quite how it came apart. Did we want him to try? Probably 3 - 4 hours of work. Our rate is $170 / hour on laptops. Wasn't sure if he could fix it or not. (He looked 14). We declined.
So, tonight, when I got home from work, I tore it apart. Cleaned it all out and put it back together. Surprise, surprise. It worked. No more stuck keyboard.