IBM AN/FSQ-7 in The President's Analyst (1967)
The computer is used by The Phone Company who plan to install communications devices in the everybody's heads. TPC's plans are foiled when Kropotkin distupts the computer system.
Computers do not catch fire without reason!
Mostly just flashing lights in a darkened room, but there are some tantalising shots of an opened wiring frame.
That rat's nest of wiring, you see the actor looking at. Was likely added by the movie's prop dept. As something the actor could mess around with, and rip out. The original wiring, is all the neatly tied up, yellow colored bundles. It was white, back in the 1960s. But yellowed with age, and heat. The colorful neon effects, showing an "E" and "54", and such. Was also added by the props dept. Or the Q-7 prop supply house.