Sounds like you got a bad CD #2. Return in to the store you got it from for another copy, or get Stardock to send you a replacement CD#2.

Well I have the same problem, except when I exchanged it the new one did the exact same thing. Any suggestions?

Well, you could just use the serial number from the CD case and download it entirely from Stardock Central.  Then you could archive the files and burn them to a CD or DVD for a backup. 

Other than that, have you tried copying the files to your hard drive and installing from there?

But I ordered a DVD version (I hope) off of ebay so hopefully the problem is solved.

You should cancel your bid immediately. Most any auctions claiming to be an "Import Version" (the only other auctions I see up right now are the UK Limited Edition, legitimate but still pre-owned), whose documentation is excluded due to being "in a foregin language" are pretty much guaranteed to be pirate copies. Moreover, even if it includes a serial (unlikely), it will have been already reigistered. And Stardock does not support the transfer of already registered serials (it is specifically prohibited in the EULA), so you'll be without support or patches as well.

If your disc is defective, your best and cheapest course of action is to simply return it for an exchange at your place of purchase as Cari recommended (as long as the store doesn't try to push off a used copy on you when you exchange, this has happened to some people). Buying a dirt-cheap copy online will most likely land you with a poor, illegitimate copy with no viable serial key.

You can identify pirated copies being sold on ebay by this text in the description. Many of the pirate auctions use the same description page, or similar descriptions and disclaimers:

* Please read: This is import edition PC video game, it plays in English, but there is some foreign writing on the game case. Manual is not in English and therefore not included. This is used game, may not work on Internet. 100% Original, factory made game, not pirated.

Why give money to criminals even at that?

Even if you're on dialup, the game is segmented into the core game, and a couple of extra downloads for the videos, tutorials, etc. The core game itself is small enough you should be able to get it on dialup if you let it run overnight (and even if not, SDC supports resuming). So you can easily get the game running, even over dialup, sooner than you can get a copy shipped off eBay anyway.

If your game only came with a single serial beginning with GC2- (it should have one like that plus another one that doesn't), you should be able to trade it in at https://www.galciv2.com/paradox. You'll be able to register with that one and download the entire game via SDC, then you can burn your own copy of the game to discs.

If your serial doesn't work on that link, contact support@stardock.com and they'll set you up as soon as they can.

If you absolutely must have working retail discs, you'll have to exchange it back at the store (but you've got a decent chance of getting another from the same batch with the same problem).