PC Shutting Down During Heavy Usage (Gameplay, Streaming)

Specs (Direct from NewEgg Bundle, bought and assembled in 2014)

CPU: AMD FX-8320 Vishera 8-Core 3.5 GHz (4.0 GHz Turbo) Socket AM3+ 125W FD8320FRHKBOX Desktop Processor
MoBo::ASUS M5A97 LE R2.0 AM3+ AMD 970 + SB950 SATA 6Gb/s USB 3.0 ATX AMD Motherboard with UEFI BIOS
PSU: Rosewill RD600 – Stallion Series 600-Watt Power Supply – ATX 12V V2.3, SLI & CrossFire-Ready
RAM: HyperX XMP Blu Red Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 Desktop Memory Model KHX16C9B1RK2/8X
GPU: SAPPHIRE DUAL-X Radeon R9 270 DirectX 11.2 100365L 2GB 256-Bit GDDR5 PCI Express 3.0 Video Card With BOOST & OC
Tower: RAIDMAX Cobra Z ATX-502WBR Black / Red Steel / Plastic ATX Mid Tower Computer Case
Storage:
Seagate Desktop HDD ST1000DM003 1TB 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive Bare Drive
PNY XLR8 2.5" 120GB SATA III Internal Solid State Drive (SSD) SSD9SC120GMDF-RB
OS: Windows 7 64 Home

Here's the Issue
About a month ago, the rig started to shutdown during periods of heavy usage (i.e. World of Warcraft, streaming video, etc.). The PC would simply shutdown suddenly without BSOD or any other sputtering or halting. The PC would then be unable to turn back on for up to 6 hours unless left unplugged. Through various posts and consulting with others on sites such as CNET, sitting in BIOS and watching the temperature of the CPU climb to almost 200 degrees in less than 5 minutes, and physically inspecting the CPU, it was determined that the most likely culprit was overheating.

I purchased MX thermal Paste, cleaned off the degraded thermal paste from the cpu, and applied MX. This resolved the issue for 2 weeks. We went on vacation last Monday, returned Sunday evening. During this week, the PC was off. I found the night that we returned that the issue on the PC has once again resumed. I do not understand how or why the issue could have been previously resolved with a fresh application of thermal paste, only to once again return so suddenly if the problem was merely overheating.

From users on CNET, I have been told the following:
Ram: not the correct type for the mobo
PSU: probably failing
MoBo: possibly failing

Seeing as how a fresh application of thermal paste completely fixed this issue for two weeks, only to have the issue return so suddenly, any ideas on what the next step in the process could be? To be perfectly honest, I would be more willing to shell out $$$ for a brand new, expensive rig rather than to buy a new PSU that may not fix the issue. I'm very much prepared (and very eager) to take this rig into my back yard and smash it to pieces with a sledgehammer. I have never had so many issues with a PC that is less than 5 years old, and I have built my own rigs many times in the past. I have been told that NewEgg bundles are frequently poorly put together and their recommended bundles should be avoided in most cases. The major issue here is possibly that the parts in the rig are not particularly compatible.

Thoughts?

Thank you Antman.

The cooling devices are as follows:

Large fan on front of tower
Standard Heatsink and Fan assembly for CPU (non liquid, came packaged with CPU)
Dual fans on GPU
Medium fan on back of tower
Large top fan on PSU
Tower is currently open on one side to aid with cooling, protected from dust by an anti-static mesh (since this problem began in the beginning of November)

Regarding GPU - the performance in gaming is sub-par by modern standards, and it does from time to time sputter, lag and stagger during gameplay. Periods of particularly intense gameplay can sometimes be accompanied by loud noise associated with the action on screen dragging and lagging. I was experiencing frequent BSOD for 6 months, but was able to identify it as a software problem, NOT GPU problem. Per your input I am actually not sure if the GPU could be associated with this and I still have my reservations about it.

Regarding PSU - although plugged into a surge protector, this is also not the first time that the PSU has caused an issue. This computer's PSU has been hit by major power surges at least 3 times that I am aware of, one of which was during a particularly powerful thunderstorm 2 years ago that caused a major problem with it. I will go into detail below:

PSU Issue #1 (2015) - power outage during a major thunderstorm. Computer would not turn on for almost a day. I unplugged it the following day and "discharged" the overcharge in the PSU by repeatedly tapping the power button, and then plugged it back in. The computer worked as normal without issue.

PSU Issue #2 (2016) - after returning from a week long vacation, during which the computer was turned off, I found that trying to turn on the computer I would be greeted with a black screen, asking me to "select boot device". This issue persisted until I unplugged the computer, and left it unplugged overnight, attempting to plug it in and power it on the next day. The PC resumed normal use at that time. I also began experience significant BSOD issues around the same time (which again, were later determined to be a result of software that was installed on the computer that was reserving memory for itself, causing Access Violations).

PSU Issue #3 (current) - began in tandem with the overheating issue a month ago. Once again, we returned home from a week long vacation, only to find that the computer had once again resumed powering off during heavy usage (i.e. gaming, streaming, etc.) as it was doing before I applied the new thermal paste to the CPU. Issue currently persists.

When the power down occurs, it is sudden - there is no BSOD, slowdown in performance, or any other indicator that something is about to happen - it just shuts down. If I try to turn the computer back on, it will attempt to power on, but will immediately shut down again. The rig won't even make it to the Windows login - power down will occur within 5 - 10 seconds of pushing power button. If I leave the computer plugged in, after several hours I can successfully power it on, but I cannot do anything other than light internet browsing or it will power down again. If I unplug it immediately and repeatedly tap the power button before plugging it back in, the computer will power on immediately, though again it will only be capable of light internet browsing or general use - any form of streaming, gameplay or slightly demanding program will cause shutdown.

Hope this info is useful.