If you have Impulse installed then I think you can right click the game in Impulse and it will give you the serial.
You might also want to try installing Impulse on the laptop and see if that will show it to you as it may be there was a glitch and your Sins registration went with Impulse rather than Stardock.
sales@stardock.com are the best people to mail. I would supply them with as much information as possible including name, address, e-mail address used, approximate date of purchase etc.
