Thank you for your post.
FileMaker Pro 8 is certified to work on Mac OS X 10.4.11. Have you tried launching FileMaker Pro 8 from a different user account? If that works, it's a good indication there is a problem with a file in your original account.
It is also possible for bad fonts to cause a problem with the launch of some older versions. Try validating the fonts on your Mac to see if any fonts are identified as problematic.
Additionally, once FileMaker is working, check your version to make sure you have the latest, which in this case would be 8.0v3.
You can find a link to the version updates on the FileMaker.com site by going to the Support menu, selecting Downloads, and selecting the "updaters archive page" under Updates and supporting files for previous versions.
Providing any other details to help narrow down the cause will help.