I tried switching card to the x8 slot, running the test with physx set to cpu, running with latest drivers, older drivers, it seems.to me that the card is not running correclty after all these...

I have/had the same problem. My card EVGA GTX 970 SC. Then i download EVGA precission software and change CPU clock offset to -190MHz and now it's ok.

Well I received my RMA, and have been using it for about a week now - this problem is solved, so it did seem like a hardware issue. The new RMA card runs Unigine Heaven (with extreme tessellation) just fine, no crashing. Same with Valley. I've played several hours of Skyrim now with no crashing, whereas the old card would crash before 5 minutes of gameplay.
 
So I am happy about EVGA's RMA policy, and that I received a new card that seems to run much more stable than the original card.
If anyone else is experiencing display crashes on GTX 970 that persist across soft reset, and must be hard reset (re-powered) to get the displays working again, I'd suggest an RMA. EVGA tech representatives seemed like they might know about this issue with some of the cards, and were not hesitant to RMA the card.
 
There is still two unrelated issues with this graphics card, that I thought might be fixed with the new card, but persist.
 
1) Occasionally, I still get a flash of an artifact across the screen, when just on the desktop/normal web browsing. The flash is very brief, and the pattern is kinda like a checkerboard pattern of white/pink that flashs over the displayed image. I've read reports of this same pattern on other people's GTX 970 and also other older nvidia cards, so I'm not sure if this is a driver issue, or a random hardware issue. It's not a big deal though, and doesn't negatively affect anything really. Oddly, the most discussion I've seen about this particular problem is on Hearthstone forums (I don't play it, just found it via google search): 
 
2) Using the DVI-I (with VGA adapter) out, the graphics card puts out noticable RF interference when the graphics card is under heavy use (gameplay). My main monitor is HDMI, and secondary monitor is the analog signal. When I start playing a game, the second monitor starts getting the horizontal waves/ripples going up and down the screen indicative of RF interference in the signal. I need to try a new VGA cable here to see if maybe the cable just isn't shielding well (could very well just be a cable issue here with bad shielding). I guess it could also be the power supply (also an EVGA product) producing the RF interference, as it would be doing its stuff when the graphics card is working more. Not really faulting the card here, as RF interference is something to deal with when using analog signal, but alas my current setup requires analog signal for a secondary monitor. 

The random black screens can also happen when using a HDMI connection, It's a driver issue, Switch to DVI and it will go away, I have a ASUS GTX 760 that does the same thing with HDMI connection using any driver past 334.89

My black screen crashes were caused by EVGA Precision X just because it was installed lol. I wasn't even using it. I also switched form HDMI to DVI because I don't use audio from HDMI anyway.

I have the evga gtx 970 superclocked and have this issue. Issued an RMA due to this thread and because of Morphe42 and Malbolja's report that the RMA helped. Will report back when I've received the new card and confirm a third time if it's just because of a faulty graphics card.

Yep I have the same issue with my card. Skyrim crashes like crazy!! Under 3 min. Here is my report from whocrashed
 
Crash dump directory: C:\Windows\Minidump

Crash dumps are enabled on your computer.

On Thu 12/11/2014 12:42:29 PM GMT your computer crashed
crash dump file: C:\Windows\Minidump\121114-17191-01.dmp
This was probably caused by the following module: (nvlddmkm+0x921828)
Bugcheck code: 0x116 (0xFFFFFA80123074E0, 0xFFFFF8800FBA6828, 0xFFFFFFFFC000009A, 0x4)
Error:
file path: C:\Windows\system32\drivers\nvlddmkm.sys
product:
company:
description: NVIDIA Windows Kernel Mode Driver, Version 344.75
Bug check description: This indicates that an attempt to reset the display driver and recover from a timeout failed.
A third party driver was identified as the probable root cause of this system error. It is suggested you look for an update for the following driver: nvlddmkm.sys (NVIDIA Windows Kernel Mode Driver, Version 344.75 , NVIDIA Corporation).
Google query:
 
I am about to run unigine heaven and see if it crashes. 

So I received my new card today and immediately swapped the 2 out for each other. Some fixes I've read in multiple threads, to name a few: direct us to uninstall and perform a clean install of Nvidia drivers, install only the graphics card driver instead of the recommended during installation, turn off v-sync during gameplay, turn off physx or geforce experience, download a program to monitor heat, bladiblah and so on and so forth. When I installed my new card, instead of gradually easing my way into the waters I just delved in, performed a clean install and installed ALL the Nvidia Drivers using the Recommended settings. The first game I had been having problems playing was Guild Wars 2 with the old card so I immediately logged in and began my game. I turned everything up to the highest settings and turned off V-sync to see if my new card would duplicate the past issue. I played for 2 hours FLAWLESSLY!!! Absolutely no hiccups! The RMA fixed my issue after my local Fry's Electronics said they had ran it through benchmarks, tests, diagnostics and blamed it on my software. 
 
I will update if anything happens but in the meantime I would recommend an RMA for anybody having this issue.

Glad this is solved for you. Good troubleshooting on your part.

I'm having the exact same problem too. My monitor stops receiving a video signal even though my computer is still running, and sound can still be heard through my headphones. Only a hard reset is able to fix it. I just talked to EVGA support to try to RMA it. Sounds like that's the only way to solve this problem unfortunately.