If the problem is indeed with the query, then it's probably this:
$db->query("INSERT INTO submitted_forms (username, rank, channel_username, video_link, video_title, video_description, video_tags, music_sources, special_requests) VALUES (''.$username.'', ''.$rank.'', ''.$c_name.'', ''.$v_link.'', ''.$v_title.'', ''.$v_desc.'', ''.$v_tags.'', ''.$m_sources.'', ''.$s_requests.'')");
I think instead, you want:
$db->query("INSERT INTO submitted_forms (username, rank, channel_username, video_link, video_title, video_description, video_tags, music_sources, special_requests) VALUES ('$username', '$rank', '$c_name', '$v_link', '$v_title', '$v_desc', '$v_tags', '$m_sources', '$s_requests')");
-- edit --
further to that, although it won't give you an error as-is, you really oughtn't insert fresh POST data in there. At the very least you probably want to use mysqli_real_escape_string on it.