Lost CD-Key, any way to retrieve?

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I also lost my CD key. I'm on a totally different PC now so regedit is out of the question. I have the manual but if I recall correctly, the CD key was on a seperate card and not on the manual...which is partly why I lost it. The back of the manual is an add for Total War: Eras.

I do have the case, the discs, the manual, the cardboard thing that goes over the case...so how exactly would I go about convincing Sega I didn't just dl the game and am begging for a key?