|I would start looking at the power supply. Random shut-downs are nearly always down to the power supply. The fact that you upgraded the graphics is a good indicator.|
It doesn't shut-down when in BIOS because there is very little load on the power supply.
Go to System properties > Startup and Recovery and make sure that Automatically Restart is un-clicked. You should then get a Blue Screen of Death giving you some indication of what the problem is.
If it still shuts down without displaying a Blue Screen of Death or you get a different indication each time then it is almost certainly the power supply.
message edited by StuartS