If your restore discs contain an image rather than a installer, your activation should remain valid between reinstalls. Just back up the sig.bin file found in the galciv2 directory and resotre it after you've reinstlaled and updated. If you completely reinstall windows though, this won't work.
Otherwise, you can activate on the laptop by this method:
1) Start the game; you will get a prompt for your serial and email. Provide them and continue.
2) It will fail to activate (of course) and ask if you'd like to activate by email. Click Yes.
3) Copy the subject line and big block of letters into a text file, or
into your email program, and save it off to portable media (CDR, USB
drive, floppy, etc).
4) Take it to a web-connected PC and send an email to
[email protected] with that subject line and content.
5) You should receive a reply with a file and some instructions; take
the file back to the non-connected PC and you should be set to go.