Yeah, it sounds like a web server configuration issue. You or the host may be able to find the reason in the site error log. If it happens only when not browsing to a specific filename, e.g. index.php, which should be a default when no filename is provided, it's possible the DirectoryIndex option is not set properly (assuming an apache server). If it happens for any URL on the site it's possible the site folders have been moved and/or the site DocumentRoot option is set wrong, or there may be a folder permission issue. An .htaccess file with certain directives could also cause it, but that's unlikely to be set up by accident. There are likely other potential causes but I'd start there.
