Troubleshooting steps I'd take with your Mac:
Clear your cache. Start SL, but do not login. Under the Edit menu in SL, go to preferences, then click the Network tab. Press the clear cache button, then restart Second Life and see if it works.
If it does not work, quit SL, and in the Finder, go to your home folder (Macintosh HD, Users, the folder with your short name on it). Open the folder named "Application Support". In there you will find a folder named "SecondLife". Move it to your desktop and try running SL again. If you have saved chat logs, they're in that folder, so save it. If you don't, then delete it.
If it still does not work, start your Mac from the OS X 10.6 DVD, and run Disk Utility. Repair Permissions and the hard drive, then reboot and try running SL again.
If it still does not work, delete the Second Life application, download it again and reinstall it.
If that does not work, restart your Mac in Safe Mode by rebooting and holding the Shift key down. It will take a lot longer to start, so be patient. Once you've logged in in Safe Mode, just restart normally and try to run Second Life.
If it still does not work, check for a hardware problem. Go to
www.apple.com/support and click the link on the right side of the screen to Download TechTool Deluxe. Burn the CD or DVD, boot from it and run the hardware diagnostics and run them all.
Your Mac is fully capable of running Second Life, just not with all the eye candy. It sounds like there's a corrupt file somewhere, probably in Second Life's cache.