I upgraded from an EVGA GTX 750 1GB to an EVGA GTX 1060 SC 6GB.  Everything works great, and I have even played several games, including Crysis 3.  That is important because Star Citizen is built using the same game engine as Crysis 3.  Also, my GTX 750 worked much better than one would expect, in Star Citizen.  By that I mean it really shouldn't run the game, but did so, at minimum.  It struggled to deliver good frame rates.
 
So I upgraded to a GTX 1060 SC.  I installed it, after deleting the drivers, then did a clean install of the drivers from the website.  Everything was fine, until I tried to actually enter the Hangar from the game's menu screen.  It loaded, and I heard the initial sounds of the hangar, but then it locked up and I heard a nasty loud buzz, then nothing.  I could not alt tab, or Ctrl Alt Delete.  I had to manually reset the computer.  Long story short, this happens when I try to enter the Universe, Hangar, Area 18, and amazingly, even when I go to the options from the game menu, and try to change the graphics quality.  As soon as I click on it...it being already set to low...the drop down appears, giving the option for low, medium, high and very high.  You don't even get a chance to change the quality.  It locks up just as if I entered the Hangar or universe.  I have to manually turn off the computer.
 
I have tried everything suggested.  I removed the USER file from the game so it could create a new one.  It never gets that far.  I reverted to the previous drivers I had with the 750.  I deleted the game and reinstalled it.  I used DDU to remove the drivers, then reinstalled them.  I checked the connections on the card.  It is installed properly, and the 6 pin power connector is installed correctly.
 
I am at a loss.  I don't know what to do.  I was so excited to get this card, and had high expectations. I feel certain it is not a card, or game issue.  I think it is something to do with my system, something in the Windows 10 environment.  I should note that I did do BoredGamer's Windows 10 tweaks, and that improved my experience with the GTX 750.  I do not know what the defaults were, or if that would even help.  This is a link to that guide. 

 
I did pretty much everything in the guide, except the SSD stuff since I do not have an SSD..yet.

HP Model: 550-040
MoBo:  IPM87-MP
CPU: i5-4460 3.2Ghz
RAM: 16GB (2x8 GB) DDR3 1600 Mhz CL11 1.5V
PWR Supply: EVGA p/n 100-W1-0600 (600W)
O/S: Windows 10
 
Entire system is less than a year old.  About 11 months. PWR Supply was added at time of purchase of the computer, as was the GTX 750
 
EDIT: The Case, MoBo, and CPU are stock.  The RAM, PWR Supply and Video Card are not.
EDIT 2:  The original PWR supply is rated at 180W at 50 degrees Celsius.  So this Pwr Supply is 420W better.

Sajin
Do steps #3 & #4 listed to see if it helps stop your locking up issue.

On my way to class.  Will do this when I get back.  Thanks in advance!  I will post results.

Thanks m0demb0y for bringing up ReShade as a problem. I tried free flight with a ReShade package installed, crashed in about 5 mins with total GPU lock up. After I exited out of the game and was back to the desktop I saw my GPU usage was pegged at 100% even though the game was closed, had to restart. I just deleted the ReShade files and hopefully that won't happen again.

m0demb0y
You did not link to the guide. Assuming it is this one? 
 
Did you do the ReShade SweetFX stuff? That would be my guess as to the source of the issue.

I only did his Windows 10 tweaks.