PC trouble, I'm at a loss here...

I like to use my PC for not just gaming, but for video editing. This means that a lot of times, my PC is left unattended for roughly hour long increments while it renders/export videos. Well, for the past month, I have had to literally baby sit it because during the exporting (heck, even during games like Prison Architect which is hardly a game that needs a beast of a rig to run...) my PC would lock up showing a strange screen (either a completely dark grey screen or a blue screen [NOT the BSOD] with lines across the screen), then the PC would turn itself off and turn back off. Of course, I always lose the work it had done forcing me to start the process over again, and like clockwork, almost every time it gets to the last 10 minutes of the export, it crashes again...

It never started doing this crap before I moved in December, and I have made sure countless times that the PC has plenty of breathing room. And hours of google searches led me nowhere. I know you guys are a largely PC centric group (in fact, it was BSN which convinced me to finally get a gaming PC in the first place which has been a great experience until 2017 when this problem started), so I definitely feel most comfortable asking you guys.

Does anyone here know what I am describing or have experienced it first hand and can help me figure out a fix? My specs are:

AMD Athlon X4 760K 3.8GHz Quad-Core Processor
Asus A88XM-E Micro ATX FM2+ Motherboard
G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory
XFX Radeon R7 265 2GB Video Card
Corsair Builder 430W 80+ Bronze Certified ATX Power Supply
and I am using Windows 10

Any help would really be appreciated, thanks