I should've researched first, as I didn't see your post. I have the same problem, and have made a post about it.

I have yet to find a solution,  and my standard SOASE serial doesn't work for entrenchment.

I bought both SOASE and Entrenchment digitally last year. Reinstalled windows a few weeks ago, tried to play Sins. "Oh, you need to activate Sins of a solar empire to play"....All fine and good, request the serial keys for the games, got the email....Got all my account information, but no serial keys. Sent in a ticket, and apparently I have no keys associated with my e-mail, which happens to be the only email I have registered with Impulse/Stardock. I even have the receipt laying about in a .txt file somewhere (should probably find that..).