...he tells him how he completely stopped aging? What's the name of the music that plays during the scene??

I believe the the scene your talking about is the one in the warehouse where he shoots Spike in the arm.
It can be seen in the following:
http://www.youtube.com/watch?v=O6L-3q4FCMs

If that is the scene your referring to then the song in the background is called Meteor
http://gh.ffshrine.org/song/2203/7

Thanks! :)