So what's your PSU like? The card you have recommends 400 Watt or greater.
If this was the problem, it would restart and shut off on an infinite loop upon turning it on.
He says
Also, it pretty much shuts down when running graphical games (blockland, minecraft, etc).
Maybe the GPU is calling for more power when running high-graphics games, thus calling for more power than the PSU can supply.
Also, companies that make pre-built computers tend to skimp on the PSU. I'm not sure if that's the case here, but it's worth a look.