I myself googled this issue and could not find a solution so i did some toying around of my own. It turns out it is a extremely simple solution.

For any that have missed my reply in an old topic posted about this, here is the solution I found.

Go into you game folder wherever you installed the game:

 .../Stardock Games/Sins of a Solar Empire/

 and look for the exe file "Activate.exe".

Rename that sucker to SDActivate.exe. Rerun the game (for me i was running entrenchment).

Now you will get a pop up window asking for "Stardock Product Activation"

Enter your email and the product serial number you got in an email from them when you bought the game you have/are trying to run. (the six-segments with 5 characters each like XXXXX-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX)

Click activate.

Congratulations! you are now running the game you payed for!

give yourself a pat on the back.

enjoy.