New computer was working, now it will not POST

The setup is:

Corsair CX 430 PSU
MSI 970-G46 Mobo
AMD FX-6300
G-Skill Ripjaws X DDR3 1600 8GB (2 sticks)
MSI GTX 650 Ti
Seagate Barracuda 1.5TB
Windows 7 64bit
Generic Lightscribe DVD drive

The computer was running fine until it powered itself off when running a game for the first time. The power LED was blinking, and it wouldn't turn back on until I switched the PSU off then on again.

I ran it again, and it shut off when I ran the game again. Temperatures seemed fine until the crash (~40c), but now it will not POST. When I turn it on, the GPU and CPU fans spin up and LEDs on the mobo light up, but nothing shows up on the monitor.

Using onboard video doesn't help, and I don't have any mobo speakers to check for beeping unfortunately, and clearing CMOS didn't help.

I have no idea what to do now.