There are couple things you can check.
First, make sure you have Build 139 of Stardock Central. You can check the build number in Help->About Stardock Central. If you do not have Build 139 you can download it from http://storage.stardock.com/files/sdcentral_setup.exe
Next, in the registrations dialog (Tools->Register Products) under games verify that your serial number for Dark Avatar is entered and is entered correct along with your email address. (Referer to your receipt for your serial number).
If that is correct then you can try to re-activate Dark Avatar (it should have been automatically when it was installed.) Locate the folder where Dark Avatar is installed. Normally it will be in C:\Program Files\Stardock\TotalGaming\GalCiv2\DarkAvatar\. And delete the Sig.Bin file.
Then using Stardock Central (restart it if you have it open), right click on Dark Avatar and select the option to "Activate Application". Upon successfully activation Dark Avatar try running it again.
Hopefully that will have fixed the problem.
There are many great features available to you once you register, including:
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