The HTTP Status Response code was a 404 Not Found error which usually means there is a problem with a URL/permalink. But just because you are seeing a 404 error visually does not really mean that is the real error that is occurring. It could be an "after the fact" error. ie X error occurs first and the final error result that is displayed is 404.
If you have access to your server logs then check the time and date the errors were occurring and send them to Go Daddy support.
Here is the most common thing that I have seen that causes this strange 404 error that is really not a 404 error.
issue/problem: the particular PHP server version that you are using is fubar. Either something went wrong when it was compiled or there is a major configuration problem.
The solution that works in 100% of these cases: switch to a different PHP server version by either using a php/php.ini htaccess handler in your root htaccess file or if the host does not use or allow php/php.ini htaccess handlers then ask them to switch your PHP server version.
In one case a person switched from PHP 5.3.x to 5.4.x and the same problem was occurring. The person switched to PHP 5.5.x and the problem was no longer occurring. You want to go up in PHP versions and not down. ie 5.3.x to 5.4.x to 5.5.x.