When ever i play a demo version of these games my computer shutsdown and when i play a downloaded full version my computer shutsdown but slightly later. for bioshock it is after the second loading screen and for stranglehold it is after the first loading screen my PC is a little low for stranglehold but should be able to handle bioshock AMD Athlon X2 4600 Evga Nvidia 7600GT 1 gig ram 320 gig HD
Most likely overheating. Download rivatuner, and monitor your temps when you load the game. Your graphics card shouldnt get over 60C
To bring your temps down? Well you can buy a new cooler, but make sure it is compatable with your card.