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.