Think logically. either Your PC has problem or CD is scrached. both can happen. I would wote for Your PC, since You did change CDs. Further on I would vote for Your CD-ROM problem. but these are just my votes.
To come to conclusion do this - make uninstall of what You have installed. insert CDs, copy it to c:// in one folder(with right mouse butt in My computer you can open the CD and copy files, instead of left butt that starts auto install). if at some point it has error or does stuck long, its CD or CD drive problem. to find exactly, try copying a different CD into your HDD, or try copying this Civ CD on different PC. most probably You will end up with new CD drive or go to shop again.
If you can copy everything allright, try to install from C://.