Computer 'restart' when playing games on high graphics.

My computer shuts down whenever I play a game that i max out the graphics on. I emailed the company I bought this computer from and it was determined to be a issue with my power supply (500W), so they sent me a new one (700W). I replaced the power supply but the issue still remains. The tech support is time consuming and stressful as they like to juggle you between branches, make you wait, and contradict each other, so I found this forum. I ran the program core temp and none of the temperatures (other than tj.max) exceed 50C. The temperatures displayed are as follow:

tj.max 105 C
power 12.5W
core 0 MAX 47 C
core 1 MAX 43 C
core 2 MAX 42 C
core 3 MAX 45 C
In game the temperature go up 2-3 C, this computer was a recent buy and when i replaced the power supply, there were no issues with dust.
My computer specs are:
1 x Processor Intel® Core™ i7-3770K Processor (4x 3.50GHz/8MB L3 Cache) - Intel Core i7-3770K w/ Intel Performance Tuning Protection
1 x Processor Cooling Corsair Hydro Series H60 Liquid CPU Cooling System - Standard 120mm Fan
1 x Memory 16 GB [4 GB X4] DDR3-1866 Memory Module - G.Skill Ripjaws X
1 x Video Card NVIDIA GeForce GTX 660 - 2GB - FREE Upgrade to 660 2GB EVGA Superclocked - Single Card
1 x Motherboard ASUS P8Z77-V LX
1 x Power Supply 700 Watt
1 x Primary Hard Drive 2 TB HARD DRIVE -- 64M Cache, 7200rpm, 6.0Gb/s - Single Drive

Thank you for any replies!

Welcome to the forums Mocking,

The temps you have listed are for the CPU, have you checked the temps for the Graphics card yet?

You can use a program called GPU-z or seeing as you have an EVGA card you should be able to use the Precision X software that comes with it.

Also have you updated your graphics card drivers from the Nvidia website.

Paul.

I have already updated the graphics card to the newest as of today. GPU-z reports temperatures of 37C with the fan at 30%. In game it peaks at around 73C at 35% fan.

Computer 'died' with these numbers:
Date 2013-05-21 23:57:43 ,
GPU Core Clock [MHz] 1136.6 ,
GPU Memory Clock [MHz] 1502.3 ,
GPU Temperature [°C] 71.0 ,
Fan Speed (%) [%] 47,
Fan Speed (RPM) [RPM] 1710,
Memory Used [MB] 556,
GPU Load [%] 51,
Memory Controller Load [%] 21 ,
Video Engine Load [%] 0,
Power Consumption [% TDP] 71.2,
VDDC [V] 1.1750

Anything suspicious in Event Viewer?

When the PC shutdowns, does it just goes out completely like you pulled the power cord out?

You using a still valid power suppressor strip?

No major voltage fluctuations in your power outlets? (Use multimeter to check)

Test your RAM sticks, act accordingly if one turns out bad.

What games are making it implode?

What's your video card power cable situation, adaptors or two 6/8's direct from the PSU?

What power supply is that 700W?

Is the clicking coming from the PSU? What brand and model is the PSU?

I read somewhere someone claimed upgrading their motherboard BIOS did the trick. [note, all settings will be defaulted, if this is done, take copious notes beforehand!]

I'd be checking for upgrades to motherboard chipset as well from motherboard manufacturer's website, ONLY. Also, called Northbridge and Southbridge drivers.

...and no I will not ask again what brand\model of PSU's these sellers gave you...

Phew, had to pull it back out just to read the label (you would think they would make it easier), anyway it's a XION, model XON-700P12N. I got it used and had to clean it out before putting it in. I just saw some reviews of it and sounds like issues i was having... like short cables and shutting off during gaming... it was one of the only probable causes but i kind of ignored it because i had a hard time believing that after sending me a system with a power supply not strong enough, they sent me a faulty power supply to replace it... would it be the PSU?

Tell em you want a decent branded psu not some pile of crap. They cut corners to save costs and supply things that ain't up to the job!
You want corsair, seasonic or Antec.