Hey Darth. That is the same error that we've been getting the last couple days. You should be able to download Stardock Central, which is kinda like their version of Steam.
Stardock Central linkInstall that then go to the My Games section. Right click on Sins of a Solar Empire and choose Register Product. The registration screen will pop up. Put your serial number in there, along with the email you already registered with, and make sure you change the drop down menu to "Sins", it defaults to "My Subscriptions" when you open the screen. Submit this and it should work. It sounds like everyone so far who tried this has succeeded.
** make sure to put the "-" in the serial number.