It is not that you have the Apps already, it's either having trouble reading the CD/DVD, or a problem on the Hard Drive... or possibly some other HW fault like RAM.
Could be many things, we should start with this...
"Try Disk Utility
1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
*Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.*
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair Disk, (not Repair Permissions). Disk Utility checks and repairs the disk."
Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive.)
Which OS have you installed.
When I got installers Tiger could be obtained on four CDs or one DVD and Leopard was only available on a single double layer DVD. I understand that some more recent versions of Leopard are split between two DVDs - probably cheaper to use two single sided DVDs!
Could you have mixed up installers and started with a single double layer DVD and tried to follow it up with DVD 2 of a later two DVD set?