Thank you for your post.
Since this is happening with local files, let's first launch FileMaker Pro and see if you can create a new database file. If so, then try opening one of the local files. If this still fails, then find another machine running FileMaker Pro and see if you can open the file.
Try uninstalling and reinstalling FileMaker Pro 10. Does this work?
Any other information you can provide about your system may be helpful.