GoDaddy is notoriously buggy when comes to Joomla hosting. But when you turn on SEF, you might have another nasty surprise, instead of your site's pages you might see this:
What you can do?
Basically you need to tweak 2 files: the .htaccess file and the active php.ini file.
If it still isn’t working or its happening less frequently move on to next file.
Locate the php.ini file in your SITEROOT directory, open it, and add to it the new line:
cgi.fix_pathinfo = 1
Save the file, upload it, and check, if the site works.