Just purchased from Steam a couple of days ago and it has never launched. At first it would bring up a dialog box for feedback to Stardock, but it quit doing that after the first day.
Please make sure you did not click to have it not show again:
https://support.stardock.com/space/SHC/1370947585/GC4+Errors+%5C+Crashes#How-do-I-get-the-in-game-crash-reporter-to-show-again?
If it then shows, please submit it with a valid email address.
If it fails, report back if you have this directory here:
\Documents\My Games\GalCiv4
If you do not, please ensure you do not have Windows Controlled Folder Access on:
https://support.microsoft.com/en-us/windows/allow-an-app-to-access-controlled-folders-b5b6627a-b008-2ca2-7931-7e51e912b034
Sean Drohan
Stardock Product Lifecycle Manager