If you haven't already done so, please try to copy the CDs to your computer first, and then install from the copy (http://us.blizzard.c...articleId=21058
This accomplishes two things - it tests the CDs integrity, and makes it easier for your computer to install WoW or TBC. If the CD fails to copy or you get an error while just copying the CD, then the CD is probably bad or damaged, and needs to be replaced. You can exchange the game or the CDs where you bought it, or you can replace the CDs through this procedure: http://us.blizzard.c...articleId=21047
Copying the CDs to your hard drive is essentially like downloading World of Warcraft. This also skips the CD reading process which can present some problems with some CD/DVD-ROM drives, and these CDs, which are highly compressed.
So if you can copy the CDs to your computer first, you've accomplished two things - you've verified the integrity of the CDs, and you've made it easier on your computer to install WoW and TBC. When you install from the copy, the installer also will not prompt to insert any CDs. The installation, if successful, will go right through, without asking to insert the next CD.
We also recommend either booting into a Selective Startup (http://us.blizzard.c...articleId=21052
), or Safe Mode (http://us.blizzard.c...articleId=21148
) before attempting to install. Either of these modes will minimize the number of programs and processes running in the background that could be interfering with the installation.
One of the main causes for installation and patching failures is mismatched or faulty RAM. If you have mixed and matched different brands and sizes of RAM, or even if you have two or more sticks of RAM, you can try removing some RAM (only if you are comfortable with working inside your computer), and install and patch with just a single stick of RAM installed. I would try this even if you have passed memory tests, as some players have reported passing memory tests, but were only able to install after removing a stick of RAM, and installing with just a single stick of RAM.
As a last resort, you can copy the entire World of Warcraft folder from another computer. If another computer has successfully installed and patched, and can enter the world without issues, you can copy over the whole World of Warcraft folder from that computer, over your network, to your computer. If you are unfamiliar with Windows File Sharing, please see the Windows Help and Support in the Start Menu.