You should be able to right click GC2 in SDC, chose the archive option, then go to Program Files\Stardock\Stardock Central\BACKUP and copy the zip it generates to CD(s). Take it along with the SDC installer to your laptop, install SDC, put the zip in Stardock Central\BACKUP like it was on your desktop, then use SDC's restore from archive option.

Since SDC also backs up the activation info when you archive, you'll need to delete the file sig.bin from the GalCiv2 directory and reactivate by the following 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 activate@stardock.com 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.