If you registered it with Stardock when you bought it, you should be able to get the key when you sign in to your account. I'm in the Galactic Civilization forum. I went to the top of the screen and clicked on Support. I then clicked on Your Downloads, which is one below the option you probably clicked, then Games and got a list of all Stardock games I have registered with Stardock.
This picture shows my original purchase of Sins of a Solar Empire.
The link to the product key in underlined in red. It did show me my product key. Notice that I can also download it if I want to.