SlayZombi :
...This problem has been happening through multiple Windows installs, meaning at least 4 fresh installs...:
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Didn't need to do 4, if one refresh install this still occurs, then the issue is totally hardware, aka the GPU is biting it.
SlayZombi :
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1. This issue especially happens when I leave my computer on with the monitor off for extended periods of time. I come back and turn the monitor on and it's a black screen as if someone pulled up a black screensaver with no way of making it display anything. The computer seems to run fine but I must force reset it to get it to display again. Lately, the BSOD's (which are something new) have been happening when I play games such as Overwatch, CSGO, or BF4. Artifacts are also sometimes present.
2. To cause the situation most of the time I can just leave the PC on and turn the monitor off for a day or so (sleep modes are disabled by the way). ....
Well the sleep mode idea was a good one, but honestly you shouldn't have the exact same issue with a fresh install.
To me it sounds like your GPU hits a point and doesn't recover, which sounds faulty. If it still has warranty I would identify these specific things I have narrowed down you post. Just saying 4 fresh installs alone will prove it isn't any software / driver / malware / etc. issue NORMALLY.
Now there is two other parts that MAY contribute to this, that I seen occur before.
1) HDD has bad sectors / failing, since the software (no matter how many reinstalls) relies on the data being ' pure ' 0 or 1 an if the HDD is giving a fuzzy 0.5 answer throws the whole thing into a tither like your having
2) PSU is poor quality - Common issue actually (see the TH articles on it). Though it may say 500W (for example) your actually getting 375W, and then when it goes into either low power state (when you walk away) or demand alot (playing games) it fails to deliver the reliable power it should.
Way to resolve this:
You need a second system / parts, either a friend, family member, or bringing it to a Mom and Pop shop. You need to test the same issues with second 'reliable' known working and replace out one item at a time. I don't remember seeing what you said you had for PSU, but I start there, then HDD. You can immediately eliminate GPU by just swapping it into another system and play the titles there and see if it causes issue.