I have hunted low and high on the net for any means of fixing this issue. I recently built a T3600 workstation as a do it all PC with a hint of gaming. 

Finally got round to downloading and playing a half decent game, Final Fantasy XIV online. I haven't had any issues otherwise until now. When I downloaded the game, it took a while, I left it for a couple of hours and when I came back both screens were black and no shake of the mouse or buttons on the keyboard would wake them, a hard reset and it turned back on just per usual. 

Now it was okay for a bit of gaming, then the day after it did it again when playing FFXIV, and now it has become more frequent to the point I can't really play FFXIV and enjoy it. 

I fully removed the driver software for the graphics card and reinstalled the latest, and this seem'd to work for a couple of hours until it did it again. The screens then refused to turn on for a while (40
mins) despite the the PC powering up, and you could hear Skype log in... I'm totally baffled.
 
 Last time the screens went black, I was keeping an eye on the temperature and it was roughly at 70 (75 highest).

I changed the default graphics card setting in the Bios from Auto to port two, which I believe mine is in. (It powered up fine)

Does anyone have any ideas, it would be greatly appreciated before I contact Nvidia.

All outputs produce the same issue, I haven't noticed any difference with the fans, the computer just kind of continues per normal in the background. (Can hear Netflix still playing etc)

Thank you for your reply.

EDIT: I have just turned down the settings on FFXIV, adjusted some minor graphics settings and turned the FPS down from 60 to 30.. GPU seems to be sat around 60 deg temperature.

Sajin
No problem. Install driver and try playing final fantasy xiv again.
 
Note: Use  (Display driver uninstaller) in safe mode to clean out all your older nvidia drivers before installing the driver I recommended. Use the clean and restart (highly recommended) option.

I'm running Windows 10 64bit - it doesn't say that driver is compatible? Should I try it anyway?

Playing FFXIV this morning on the lower settings and it still black screen'd and was running around 70 degrees temp.
 
I did a clean wipe, installed that software as directed and it wouldn't detect my other screen, and stayed at low resolution. I guess because it's not compatible with windows 10? 

I have found 353.62 driver, and will try installing that.

It just black screen'd after 5 minutes of game play but the whole PC crashed, it made the little error noise then no sound and black screens.. Can't believe I spent £600 on a graphics card to have issues like this! 

I read somewhere that someone else had a similar issue and could have been the ram..?

also with  ffxiv   did you look up any things as this with that game ?
 
http://forum.square-enix.com/ffxiv/threads/325160-FFXIV-causing-black-screen-hard-crash-Windows-10-64bit
 
https://forums.geforce.com/default/topic/1003165/gtx-1070-loading-ffxiv-to-blinking-black-screen-4k-monitor/
 
 
what also gives this issue ?   everything you try to run ? 
 
what about the pci-e power plugs ?  are you using them as correct ?
 
[kinda like whats said fron these ? ]
 
https://www.dell.com/community/Desktops-General/8-pin-power-in-T3600/td-p/4178841
 
https://www.dell.com/community/Desktops-General/GTX970-in-Precision-T5500/td-p/4529720
 
https://www.dell.com/community/Desktops-General/GTX-760-on-Dell-Precision-T3600-8-pin-6-pin/td-p/4192539
 
 
 
one thing with a prebuilt like dell  or hp , ect...  + you use a workstation   you  got to be sure the mothebords bios will fully support any card you stick in it  .   see with all that you got the consumer ''gaming'' vid cards  may not handshake .  
 
quite a few buy these cards and stick them is prebuilts to find they not supported under the bords bios   or may need a latest boards bios update to help with support of graphics cards  .   this was pretty common whit the release of the 900 series cards  . heck guys with older custom builds like a z68  found these cards may not work in them with out a bios up date   or some brands of cards  [ evga the most ]   and swapped for the same card from say MSI and it worked   [maybe something in the card bios as well betewn brands  to make that ''handshake '' ? ]
 
some models from dell are not so upgrade friendly   
 
from this list you don't see any ''gaming cards''  under video  ?
 
http://www.dell.com/support/article/us/en/19/sln290703/the-hardware-specifications-for-the-precision-t3600-desktop-workstation?lang=en#Video
 
 
thing is when you upgrade out side of what dell officially supports and listed parts your doing that at your own risk  ..  dell guarantees   only what they support  for parts and upgrades  not a drop more .
if it works  then great,   if not oh well  .. there sold guaranteed to work  as is out of the box new with what dell put in it  , that's all .
 
this guy got a 970 working in his with win-8 , but don't list psu or what not ?
 
https://www.youtube.com/watch?v=O5s6ss4zzPs
 
try what sajin said above and hope for the best
 
good luck 

Dr Death, thank you for your comment, it's given me a lot to think about.

I actually had a friends dad build it up for me.. and one of the connectors for the power supply to the Graphics card is just a two pin which looks like it's been cut down.

What I'm going to do is order up some adapters (a selection) and see if those make any difference (2x6 PCI-E - 8 pin) etc.. 

Thank you ever so much for your help - it is muchly appreciated.

Photo 1

 
Photo 2

 
Photo 3

I've ordered 6 different adapters.. so I will keep you posted on that front.

However, I have turned off a few other graphics options (shadowing & some detail) and also running FFXIV in a smaller window keeps the GPU on low demand. 11% power consumption, jumps to 35-45% if I run the game in full screen. It's yet to black screen on me, but I should hope so with graphics settings so low..

Yep, try to find a good driver that wont crash, usually much older drivers, and also use MSI Afterburner to put your fan speeds up to 100% while gaming (turn it off when you arent gaming).