http://www.apple.com/support/

It has a serial number form on the right hand side towards the bottom. Plug it in there and it will tell you the warranty status.

If it is slightly outside the window, i'd let them know how long this issue has existed. It seems the drive or something has been bad for a while, and you were working around it by lowering the burn speed. In all my time of owning a mac with a CD burner (2002), I have never had a burn process lock the system. Even when the burner did go out in my old G4 Cube, it would just report some error on the attempt and move on.