You can delete the files extensions.* (extensions.rdf, extensions.cache, extensions.ini, extensions.sqlite) and compatibility.ini in the Firefox profile folder to reset the extensions registry. New files will be created when required.

See "Corrupt extension files": http://kb.mozillazine.org/Unable_to_install_themes_or_extensions

If you see disabled extensions that are not compatible on the next start in "Tools > Add-ons > Extensions" then click the "Find Updates" button to do a compatibility check.

Thanks for the help, but when I start firefox after I have deleted the files it immediately creates new files and does not successfully start. No error message or anything.

Does that happen with every extension?

If you start with installing the same extension then try a different one.

Did you try to uninstall (trash) Firefox and reinstall that application ?