Today, I decided to replace my Radeon HD 5870 with my older GeForce 275, to see if it also makes Crysis 2 shut down my computer at a specific point in the game. Whaddayaknow, it didn't! I'm going to try out AVA and Project Calypso later on and see if the issues I was having in those games (similar shutdowns) are still present. If not, then I guess the mystery is solved: a faulty gfx card.