What causes everything to go wrong in Alphaville?

I initially assumed that Lemmy's riddle, like he said it would, caused the computer to destroy itself if solved. But there is a significant gap between the riddle and when things start to go really wrong (or was it more of a gradual thing?), although I suppose it could have taken the computer time to figure the riddle, or at least some time between self-destructing and things starting to go wrong. So if anyone can explain this a little better it would be greatly appreciated, thanks.