@Sarcastic
It could be literally anything, even a software problem. If there's no error message to go off I'd just be stabbing in the dark.
The first thing I would do is go spelunking in the Windows Event viewer.
What Is the Windows Event Viewer, and How Can I Use It?
The log for Application and System are where most messages end up. You can compare the timestamp on the events to the last time you're computer had a conniption, that way you don't have to search ALL the events.
There's always Memtest86
MemTest86 - Download now!
I'd run it up to 24 hours (or at least overnight) until you either hit an error message or it passes.
If you have more than one memory module you could always pop one out, run on it alone and see if the other module was the source of the fault. Then do the same for the other module.
Testing a GPU is harder in the sense that your onboard won't cut it for most gaming, but you could just run on the onboard graphics for desktop stuff and see if it still happens. I'm inclined to think it's not the graphics card so I'd try other things first.
Hard drives can completely cause a system halt, Download seatools (your specs had a seagate hdd) and run the tests:
https://www.seagate.com/support/downloads/seatools/
Get Seatools for DOS, running it in windows is possible but not the best way to test, you'll need an optical drive or to create a bootable USB drive out of an ISO. There are 3 tests I usually run but the names escape me. I think it's the short, long, and there's a seagate specific test.
If you have another hard drive laying around, Install the OS clean on that drive and see what your system does.