Computer powering off on its own

Just finished a i7 build and it is having some problems.
specs: i7 3770k
680 gtx 4G
16G RAM 1866
asus sabertooth z77
WD Green 1T
120 G SSD sandisk
cx600 PSU
Zalman cooler 92mm
corsair c70 vengeance

After playing games for a little (10-30 minutes) the computer will power off with out a warning or error. Next the computer will click on for a fraction of a second, and then power off for good. If you try to turn on the computer again it will click on and off as well. After waiting a little the computer will finally turn back on and work for another hour then the problem will repeat. I have swapped the power supply for an ax1200i, I have changed the gpu to a HD6970, and changed the mother board and ram to an old 1366 i7-920 with 12g of dell ram (1066) and changed to cooler to and old corsair v8. I still get the same result. Their is no overclocking and i set the 16G of corsair ram to default. The bios for both motherboards is also at default.

What kind of temperatures are reported by the motherboard, GPU, and CPU under load?

Is cm coolermaster?
And if so what model is it and how old (yes powersupplys do age)?
Is it a new powersupply?

Asking because coolermaster have made a bunch off really crappy powersupplys (and some really good ones) so just saying cm is like saying i have a Chevy (as in you have too guess from everything made from 1911 until today).
The crappy ones can die after a year or they can work for many years it is a gamble since the quality is all over the place.

under load cpu is 50c and gpu is 85c

correction its a cx600 its old, probably 5 years, but i did try a new ax1200i that's less than 6 moth old

Corsairs CX and CS series is pretty crappy and i would not use it at all anymore because i do not have the money to buy new stuff like cpu/gpu(memory/motherboard/ssd/hd IF the psu take anything with it in death.
And it is NOT a question of IF it will die it WILL die and when they get 2-3 year old it is pretty common that they die.
Lots and lots of people have had that happen with Corsairs CX/CS series and it is not uncommon that the psu takes something with it when it dies.

So stop using it NOW take it out throw it away before it harm/kills anything else!!!
The chance that it already have harmed something in your computer is pretty high since your having trouble even with a new'ish GOOD psu.
The question is what and to find out it is test every part on another computer one by one until you find what is bad or is lucky and nothing is.

Switching your power supply would be a good bet, did you have the same problem with your ax1200i?

No, the 1200i was in perfect working condition before I put it in the current build. The build it was in was a x79 with cross fired cards and i had power to spare, with OC as well.

I am going to tare the computer apart and run it on my bench and do one component at a time to see if I can figure anything out.

Ok, I have solved the issue. It was my AX1200i, it has A faulty rail and was causing the computer to power off. Thanks to everyone for all your help!