The person you are thinking of is Charles Whitman. He was notorious for his shooting spree from the top of the tower on the University of Texas campus on August 1, 1966. Ex-marine sniper with brain tumor leading to that behavior (killed 14 people and injured dozens in around 90 minutes, before police shot him dead).
I know there is an old movie about the incident, but I checked IMDB and could not find it (they have a documentary about the event listed, but not the old movie about that). Anyone remember the name of the movie off hand? I hate when I should remember something but can't; it will bug me for the rest of the day now.