[eluser]CroNiX[/eluser]
That's a security feature so that someone can't call your model (or anything else like controllers, etc) directly from the URL. BASEPATH gets defined at the bottom of index.php and CI uses it all over the place internally, so it should exist since everything routes through index.php before anything else.
You may have gotten it working, but most likely you have a bigger issue going on and you now have opened a security hole. I'd advise you to keep looking for the cause.
If you google "codeigniter godaddy", you will see plenty of issues with them as a host, and some workarounds. Personally, I'd never use them as they don't seem to have a standard setup.