Based on what you've posted, it's not at all clear to me what could be causing the problem. (Perhaps you've left some stuff out?)

If it's the case that you're getting reports about not being able to pass tests during the installation process, this can happen if you've assigned a password for the mysql root user account (as per the recommendations in the mysql installation), but forgot to provide the password when starting up the DBD::mysql installation. In this case, the tests fail because the "make test" portion of the install can't connect to the mysql server. (Of course, this also assumes that the mysql daemons are actually running when you install DBD.)

I apologize for being a little foggy on the exact manner for specifying the connection info, but the module docs and/or other monks should be able to help, if that's the problem.