I did some hunting around and got some feedback through another forum. It was suggested that the window manager had crash. Since I'm running GNOME 2.30.2, I was told to run the following:
metacity --replace &
This worked temporarily. As soon as I closed the terminal, the symptons returned in full. Next, I was asked to run the following:
nohup metacity --replace &
This worked better. I could now open and close windows, and everything worked as advertised. However, once I log off, the symptoms return again.