I suggest you refer to this video:
But set that aside, what makes you so sure it's a graphics issue?
There are quite a few other possibilities, such as:
1. A CPU overheating problem (this could definitely make it power off at random), but if you're saying it just switches off right after powering it up, that's unlikely to be the issue.
2. A bad power button on the case (you could switch it for the reset button for testing)
3. A bad power supply (try another?)
4. A short between the motherboard to the case (if it's lacking in standoffs), try testing it outside the case sitting on a cardboard.
5. A motherboard issue (such as a bad cap or mosfet)