I have this exact same problem, or at least I think so.
I bought SoaSE Trinity a couple of months ago, got the serial and it worked. I've been playing for quite some time now. However, I live with several siblings who also use the computer, and since I only had impulse on one computer, I had decided to install it on another so that I could play the game on one of the other PCs in the house.
However, upon installing it, the only game it listed under "My Games" was Prometheus, which I had indeed installed sometime after Sins. However, I couldn't find Sins, and when I emailed for the serial to be sent back to me, it only had the serial for Prometheus listed. So I went to the PC which I had originally installed Sins, and checked it, and sure enough, it was still there, registered and all. So I wrote down the serial code and went to "Register Product".
However, when I punched the code in (I was sure to leave out the "-"), it said, and I quote, "The serial number you have entered is not recognized by Impulse. Only serial numbers provided by Stardock will be accepted. Please check your selected product, email address and serial number, then try again (ref: 2)" And so I did, about six times - and each time, I got the same error message. I don't know what to do here.