The last time I played a Space Quest game that wasn't SQ6, I think it was 4 or 5. There was a really big problem with the game killing me within a few seconds because the processor was making the game act as if time was speed up - Someone comes and kills you if you idle too long, I think it was.

Regardless, I obviously wasn't able to play the game. I seem to recall this being an issue with one of the King's Quest games for a while back in the day. Has anyone encountered something like this with the GOG versions?

I know some games, like 7th Guest, had a problem with modern (compared to its release time) computers simply being too fast to play the game reasonably. In 7th Guest you had the Amoeba/Othello game, in which the faster CPUs cause it to become so "intelligent" it could never lose.

Sounds like Space Quest 4, where hostile cyborg can kill Roger if he doesn't escape in time. All Space Quest games are DOS games and GOG uses DOSBox to run them. You shouldn't have speed issues with them, but if you do then it's easy to change speed in DOSBox configuration file.