The No input file specified is a message you are presented with because of the implementation of PHP on your server, which in this case indicates a CGI implementation (can be verified with phpinfo()).
Now, to properly explain this, you need to have some basic understanding on how your system works with URL's. Based on your .htaccess file, it seems that your CMS expects the URL to passed along as a PATH_INFO variable. CGI and FastCGI implementations do not have PATH_INFO available, so when trying to pass the URI along, PHP fails with that message.
We need to find an alternative.
One option is to try and fix this. Looking into the documentation for core php.ini directives you can see that you can change the workings for your implementation. Although, GoDaddy probably won't allow you to change PHP settings on a shared enviroment.
We need to find an alternative to modifying PHP settings
Looking into system/uri.php on line 40, you will see that the CMS attempts two types of URI detection - the first being PATH_INFO, which we just learned won't work - the other being the REQUEST_URI.
This should basically, be enough - but the parsing of the URI passed, will cause you more trouble, as the URI, which you could pass to REQUEST_URI variable, forces parse_url() to only return the URL path - which basically puts you back to zero.
Now, there's actually only one possibilty left - and that's changing the core of the CMS. The URI detection part is insufficient.
Add QUERY_STRING to the array on line 40 as the first element in system/uri.php and change your .htaccess to look like this:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?/$1 [L]
This will pass the URI you request to index.php as QUERY_STRING and have the URI detection to find it.
This, on the other hand, makes it impossible to update the CMS without changing core files till this have been fixed. That sucks...
Need a better option?
Find a better CMS.