The Connection Machine, a 65,536-processor parallel computer designed in the mid-1980s, was a black cube with one side covered with a grid of red blinkenlights; the sales demo had them evolving Conway's Game of Life patterns.
Which made me think, immediately, of The Thing from the Bromeliad Trilogy. The Thing is a small black box, which serves as a flight computer and general thinking machine for the nomes.
From the picture on wikipedia, it looks like something like that, with lots of 'blinkenlights' could easily have inspired Pratchett's description of a futuristic computer. Has he ever cited inspiration for The Thing, or made similar references that might hint at such a fact?