I recently purchased an ASUS G74sx from ebay. After i had set it up, it blue screened of death on me. I tried starting it up a while later and after about 20 minutes it did it again. I started it up again and began installing new GPU driver update along with some other essential programs. (google chrome, norton anti virus, winrar,). While i was installing SWTOR, i left and came back to it a little later to find it turning on and off (power button keeps lighting up and it makes a sound). I had to cut off all power sources to make it stop. Now when i try to turn it on, it lights up and makes a little sound as mentioned before. Then it turns straight back off. Can't get it to turn on now.
Also check that your drivers are properly installed, drivers can cause the system to BSOD also, you can check the BSOD code and type it into google to find out what its related to.
My personal thought is that its overheating, download a program called "speccy" this will give you detailed information about your hardware and the temperatures its running. Switch the machine on and leave it run, monitor the temp and if it starts burning up i would recommend some artic silver paste on the cpu / gpu.