Random "crashes" where everything is fine except display

Hello everyone.
I am struggling with strange problem. I dug through so many forums and websites to get some answers, unfortunately none was unequivocal.

From time to time my computer is crashing in the way that sometimes the screen is frozen, however the music/sound is still being played in the background without any distortions; sometimes the screen is blank, all black, "no video output" as my display is telling me; totally like the output from my graphics card is turned off - the rest is still functioning - e.g. the is still sound and even I can still "play" a game - I mean I hear sounds of footsteps when I press arrow keys. Those crashes were quite often in the past week, what is more, I didn't have video output after reseting my PC! No video output from the very beginning I pressed a power button - even didn't have MSI motherboard logo/peripherals initialization.

I decided to run my PC few days on an integrated Intel HD chipset; in the meantime I completely removed Nvidia drivers and all traces of it by running a DDU utility software; it is worth to mention that I never had the newset drivers, I was running some old versions due to a common problem "the driver has stopped working..." in the more distant past. So, my GeForce 660 was turned off in BIOS during my usage of Intel HD, and in the last 2 days I even removed it completely from my PC and put it on my desk. In fact I was going to test it in my friend's rig. An hour before I was about to go to him I put the GeForce inside my rig, installed the newest Nvidia drivers and started using my PC - mainly youtube and web surfing. No crashes. Then I played a game for a few minutes - and suddenly black screen... but a few seconds later screen came back with info "the driver has stopped working..." - however please read further and let's assume now that this particular issue was related only to bad Nvidia drivers and wasn't related to my main problem I am describing here, besides it happened only once (as for this issue with "driver has stopped working..." - I read once it might be caused by having "PCIe Link State Power Management" turned on, in fact I turned it off in the past and didn't have those kind of problems anymore on my old drivers).

But to the point - today I ran some stress tests using "HeavyLoad" utility software. I tested CPU and CPU separately and then also together, tested also RAM. No crashes, even when my CPU reached 75 degrees (Celsius). Then I played "Ori and the Blind Forest" (great game by the way!) and after few minutes the screen froze, but sound was still being played - I waited for 15 seconds and rebooted my PC; another try, the same game - 10 minutes or so passed and the screen turned totally black and "no output from HDMI" - the sound still being played. I rebooted again praying I will have an output after I pressed the "reset" button - and I think my prayers worked, because my PC booted normally to Windows with display on. Third try - this time I played for 30 minutes - no crashes. Now I am writing this post from the same PC and still no crashes.

I don't want to suggest anything but after analyzing and rethinking all of this and running aforementioned tests (like DDU) I think we can rule out the PSU malfunctioning (besides I don't believe it could crash, I have SeaSonic Bronze 620W for 2,5 years, and honestly I don't think I am using more than half of that power). My gut tells me it can be hardware issue with graphics card or motherboard, and after adding some reasoning biasing towards graphics card since I have problems only with display (freezing or turning off) than anything else.
However yesterday after having fresh-installed the newest Nvidia drivers I started to think that maybe it is more software- than hardware-related issue... But to further support this thesis there is one thing I should know - if a display driver fails should it or should it NOT affect also displaying the POST screen (I mean the first screen we see after turning on a PC)? I think the POST screen is displayed BEFORE any other driver is loaded, but maybe I am terribly wrong here.


What else I did trying to get rid of my problem:
- uninstalled drivers for Realtek Audio HD since I am using good ol' PCI Audigy SE (ok, ok, it was never a good card...) - I read on one forum that having installed drivers for integrated Realtek and also standalone sound card could cause crashes.
- interchanged RAM modules in their slots
- re-seated graphics card and blew out dust from radiator and fans

Some additional info and my PC configuration:
- I did NOT hear any "beeps" during booting even once. Nothing.
- I have never overclocked anything
- CPU: Intel Core i5-4670
- GPU: MSI GeForce 660 OC Twin Frozr
- MOBO: MSI H87-G41 PC Mate
- RAM: 2 x 4GB Kingston HyperX (DDR3 I think)

Thank you for your patience and for reading my whole and certainly too long post.
Any help is much appreciated.