Are you shutting down all non-essential programs (especially anti-virus) before trying to install the game?
Try a different optical drive, if possible. Another drive may be better at reading the disk, or the one you tried could be starting to fail. If you bought the game at a computer store, or a game store with a demo system set up, they should be willing to check if the disk is readable there.
If you have access to a different computer where the game installs ok, you might be able to copy the game folder over to your main system (over a network or USB drive, etc).
In Windows Explorer, try manually copying the DVD contents to a folder on the hard drive. I don't know if the install will work from the hard drive, but if you can copy the files ok that would probably rule out a problem with the disk itself.
Another person had a conflict with a new (when D2:ED was released) optical drive:
Can't install. You could check your drive manufacturer's site and see if there is a firmware update (which may contain compatibility updates, etc).