BSODs when running games: Is my laptop graphics chip dying?

Akilae

For quite a while now I've been running games on my laptop without any problems. A while ago I updated drivers on my laptop to play Bioshock Infinite, and things ran well. Last night I played a session of Borderlands 2, which was fine if a tad bit stuttery, then set the laptop aside for the rest of the night. This morning, firing up Borderlands 2 again, the game froze at the "This is the save icon..." screen, resulting in a hard lock. I thought it was odd, and had to force the laptop to shutdown using the power button. A few more tries result in the same thing. Steam game cache check also turned up fine. Uh oh.

I tried running other games. Bioshock Infinite, Diablo 3... even Minecraft. All give me BSODs pointing at the graphics driver whenever things get graphically intensive.

UPDATE: Apparently Simcity 4 and Kerbal Space Program still work.

I decide to update drivers, just in case it was a driver problem, and now I get this:

Hardware malfunction
Call your hardware vendor for support
NMI: Parity Check / Memory Parity Error
The system has halted

Nothing else makes this problem occur. Streaming and movies are fine.

Should I start shopping for a new laptop right now before everything dies on me?

Draygo

What is the chipset specifically?
Nvidia? ATI/AMD?
Laptop make and model?