Yep, I thought that might be the problem. mod_fcgid, which is FastCGI, which is known to be problematic for WordPress and all PHP site types: WordPress, Joomla, every other PHP site type on the Planet, is the cause of the 500 errors. The good news is there is a solution, which allows you to keep using FastCGI instead of disabling it.
Have your Host go to the link below and add these Server configuration changes in the Server’s httpd.conf file.
http://forum.ait-pro.com/forums/topic/go-daddy-php5-3-php-ini-file-zendguard-loader/#post-12965
If your Host needs more information on what the problem is and why the Server config fix is necessary for this known issue. Then send them this link, which has my research on this known problem.
If for some reason your Host cannot correct this issue on their Server then you will need to disable FastCGI in your Control panel. FastCGI 500 errors will occur intermittently/randomly on your website, unless the Server configuration changes have been made in the links that I posted above.