If you can copy the files off the DVD, that implies the DVD is working and is not defective. Can you copy the files from wherever you put them on your computer into the X-Plane install?
Also double check that the installer is asking for DVD 2 and not a different disc. It will not warn you if you put the wrong DVD in. Also make sure you aren't installing into a protected location or to an install where you don't have write permissions.