So just to be clear when you tested GalCiv 1 with your GTX 770 were you operating with Windows 10 or Windows 7/8. All this used to work just fine for me when I was using Windows 8.1.
I just uninstalled/reinstalled GalCiv 1 and it made no difference. The game is installed on the C: drive along with all my other Steam games.
I tried all the available compatibility modes without success. I also tried to run as administrator and the other resolutions, all also without success.
My Steam version of GalCiv 1 worked just fine with Windows 8.1. Yesterday I upgraded to Windows 10 and all my Steam games except GalCiv 1 start just fine. I have the latest video driver for my GTX 770 card. When I start GalCiv 1 the screen goes black for a second or so and then I'm returned to my desktop.