Computers have been around for a long time but when did mainstream digital computers really begin to appear in TV shows or films? I believe this is inline and similar with this question.
From IMDB synopsis: "Two novice thieves are plotting to rob a bank in Vancouver. A photographer snaps a shot of one thief as he is carrying the bank building's blueprints. The would-be thief then begins a relationship with the photographer and attempts to retrieve the photos. Meanwhile, the thieves' plot consists of this: one man will enter the bank building after dark, while the other man sits in a van and uses a computer to unlock the building's doors."
The first consumer grade computer used for a character's personal endeavors as opposed to the quasi-business use above was an Apple II in Evilspeak (1981).
Large mainframe computers began showing up in films as early as the mid 1950s.