Please go through the troubleshooting guide and if you still have issues there's instructions on how to submit a support ticket so we can look into it.

https://esupport.stardock.com/index.php?/default_import/Knowledgebase/Article/View/496/161/general-galactic-civilizations-iii-troubleshooting

@OP: Instead of waiting for support to reply (like in forever), I did some digging myself. After finding a 226 error for a library (= usually 'missing dependency'), I started up DXAtlasWin.exe, and noticed it was missing MSVCP110.dll, which is part of a VisualStudio redist package (that got apparently uninstalled when I had STEAM uninstall an early-access game). After reinstalling the distro, my game started up normally again.

You can find the distro here: http://www.microsoft.com/en-au/download/confirmation.aspx?id=30679

Maybe this will work for you too?!