WAR GAMES, 1983

Director: John Badham 

Writers: Lawrence Lasker and Walter F. Parkes 
Stars: Matthew Broderick, Ally Sheedy and John Wood 
Plot: A young computer whizz kid accidentally connects into a top secret super-computer which has complete control over the U.S. nuclear arsenal. It challenges him to a game between America and Russia, and he innocently starts the countdown to World War 3. Can he convince the computer he wanted to play a game and not the real thing? 

War games trailer 

 

Recommendations: Primer, 2004 is another good flim about computers.