It is most likely that the problem that you are having is due to a security update that MSFT released last fall. Among other things it prevented the copy protection scheme used by many older games, including CIV, from working properly. The result is that when the game tries to access the copy protection program to verify the disc, it is unable to do so and the game won't start up. Using Windows 7, you can work around the problem, in order to get the game to start up. The work around is discussed in the thread "Please login with administrator privileges and try again" below in this forum.
For Windows 10, the work around will no longer work because MSFT removed the copy protection software entirely, rather than turning it off, which is what the Windows 7 patch did.
However, the "Beyond the Sword" (BTS) expansion disc for the game, with the game patch 3.19, will work on Windows 10 because BTS patched to 3.19 no longer uses any copy protection, so it works fine without the work around. You can download the 3.19 patch for free from the "Patch & Update" section of these forums.
The final option, which probably won't do you much good, is to buy the download online version of CIV from one of the content providers, such as Steam. Those don't use the now deactivated copy protection scheme.