Well, at the top of this page, click My Acount and then click on Registrations.
Another option is to try and email support@stardock.com with whatever email account you may have registered the game with for them to send the serial key to you.
Your serial key, if registered, is linked to an email address. So it should be as easy as figuring out which email address you had used to register back then...
If all that doesn't work, begging, pleading, sending a case of beer to SD headquarters all might help.
Buuut in other news, lets see if we can figure out whats up with the crashing end of things. Boot up the game fresh, make it crash, then go to the folder where galciv2.exe is located (may vary by OS or such..check the shortcut for the game), and open up the file called "debugg.err" and copy/paste the entire contents of that here.
One other thought. If you make a fresh game does this crash still?