What does it say in your console log in /Applications/Utilities/console? If you have anything less than 10.3.9 (check the apple menu and click About This Mac), you need to upgrade to that before Blender will run.
So you’re running the powerpc version of Blender on system 10.4+? and you only get the two lines:
can’t open library
doesn’t map to a codespace range
exactly at the bottom of the console log and those lines appear every time you launch Blender?
Try the following steps:
open the terminal (/Applications/Utilities/terminal)
right-click the Blender icon and select show package contents and go to contents/MacOS
in the terminal, type cd and drag in the folder MacOS and hit return
Now type in ./blender -debug and hit return
post the output from the terminal window.