How can I install os on a mac mini with a mac os x install DVD
A Mac Mini OSX Install DVD supports the particular release of Mac Mini with which it was released, not all Mac Minis. The fact that your Mac Mini does not have a DVD slot suggests that it likely did not ship with that install DVD. Additionally, in general, Apple hardware does not support installing versions of Mac OS X older than the version current when the hardware was released.

This may be the source of your problem.