PC crashes while gaming

I built a computer 2 years ago that worked great until recently it started turning off by itself. The computer only does this while gaming. What happens is the screen freezes for a few seconds with a buzzing sound then the computer turns off. Sometimes there isn't a buzzing sound or frozen screen but it still instantly turns off as well. Most of the time when this happens the computer attempts to turn itself back on again then it fails to do so. I know this since I hear the usual click and fans whirring then it's dead silent a few seconds later. It does this repeatedly unless the power supply switch is off. This video is similar to what happens [video="https://www.youtube.com/watch?v=sJ3yXpY5yoc"][/video]
Any way to diagnose the issue? I haven't reapplied thermal paste to the CPU this entire time and the temps while gaming never go above 60c for both the GPU and CPU. Also, the blue light on the motherboard near the CPU socket is off when it turns off yet the GPU still has two green lights on next to the two 8 pin connectors.

- PC Specifications -
GIGABYTE z97x-ud3h motherboard
ASUS GTX 780 Ti graphics processing unit
8 GB DDR3 random-access memory
Intel i5-4690k central processing unit
Thermaltake Toughpower Grand 1200w power supply
Windows 10 Pro 64-bit

EDIT 1: I read here that a faulty PSU can damage other components so will purchase another. Is there any brand that usually is of good quality for power supplies?
EDIT 2: I've read more topics relating to my problem and tried both windows memory diagnostic tool (pc turned off during it and stayed that way for a while) and memtest86 (froze after 2 minutes). From my view it seems that the memory is an issue as well. I also remember once out of more than twenty crashes that I had a BSOD that mentioned something about the memory and voltage. Another note is I actually borrowed this memory from a pre-built PC purchased circa 2010, rest of components were purchased mid-2013.
EDIT 3: I've tried a fresh install of graphics drivers for my GPU, no luck. Also updated the BIOS in the motherboard to most recent non-beta update, still no luck.