Computer Randomly Shuts Off (Please read)

I'll start by explaining this from the beginning. I purchased a pre-built PC from Newegg around late 2013. I didn't have so many problems with it. It ran perfect and there would be times (though they were rare) that it would shut off randomly, but not like this. My PC had a huge problem prior and I just replaced the graphics card and while it did resolve the issue, there was another I was not aware of. The problem my PC had, was that there was no image showing. This was most definitely due to a power surge occurring. I connected my TV to a power outlet and when I did there were sparks everywhere and it was pretty bad. TV was fried and anything that was connected via HDMI messed up. I use an HDMI splitter for pretty much anything and anything that was connected to it during the power surge, it messed up the HDMI for them. My PS4 was connected via HDMI and while it did work via remote play on the Vita, it showed no image on the TV whatsoever. Same case w/ PS3 (had to use component cables to show an image.) After not using my PC for a while I noticed my PC had the same issue. I tried everything from removing the CMOs battery, waiting five minutes and putting it back in, to changing the slot where the GPU went. Nothing. Just recently I bought a GTX 960 2GB and after installing it, an image showed, but now what happens is that it seems the computer shuts off entirely out of the blue. I downloaded Windows 10 right after it worked so I wasn't able to deduce if it may be a problem with the OS. Regardless, I went and downloaded a ton of games on Steam, Origin, and Uplay. Started downloading it League and Guild Wars 2 and next thing you know it the PC shuts off. Played Blacklist after it finished downloading and it shut off at a particular loading screen. I was able to play it once, but once I was back to the loading screen it shut off. It seems like when the PC is doing a lot of activities at once, it seems to randomly shut off. I just played Tomb Raider maxed out and it was running perfect for two hours until it shut off when I pressed CTRL+TAB to go back to the Desktop screen while playing. Before that though, I left it on overnight to download games and it didn't shut off at all. I genuinely can't figure out the problem. Whether it's an issue with the motherboard, the power supply, or the CPU. I know I wrote quite a lot, but I sincerely thank anyone who's read up to this point. Here are the specs along with the link to the Newegg item.

Processor: AMD FX-8350 4.0GHz
Memory: 16GB DDR3 1600
Storage: 1TB SATA III 7200RPM
Optical Drive: 24X DL DVD+/-RW Drive
Graphics: NVIDIA Geforce GTX 960 2GB GDDR5
Power Supply: 650W 80plus bronze certified power (I tried looking up what the PSU was, and it says "GreenMe"? I did a bit of research and I found the PSU: http://www.thinkcomputers.org/reviews/inwin_greenme_650w/5.jpg )
Operating System: Windows 10 64-bit
Motherboard: Chipset AMD 970
CPU: AMD FX-8350

Newegg: http://www.newegg.com/Product/Product.aspx?Item=N82E16883258050