It runs fine on my 760 gtx. You should ensure that the game is using your high-performance card. There is a GPU notifaction icon you can turn on to ensure that it is actually using it. Be sure that you individual .exe is not set to use the intel HD card. You should update your intel HD drivers in case they are out of date as this may cause some problems.
Ensure you are running no other programs when you run GalCiv3, try to run as few things as possible.
Try running the game immediately after you reboot your computer.
Try running the program in lower resolutions. Try running the program in full screen with your laptops recommended resolution.
Ensure that your computer is in a cool place and is relatively cool, sometimes your computer will slow down its performance to ensure that the computer won't overheat.
Run the game with the laptop plugged in. There are other power settings that may override your settings. In other words, your nVidia card will not be running if you are running on battery power and you have the settings not set for High Performance, but battery saver.
These are my best suggestions beyond updating drivers in your computer in general.
Also, you should send a support ticket to Stardock to see if they can help resolve your issues.
There are a lot of tests you can perform to see if some of your hardware is actually working. I.e. test the ram for errors, test the hard drive for errors, benchmark the video card to ensure that it is working. Note that these hardware tests will take a LOT of time and you should try the above before messing with testing the hardware.