$this->form_validation->run() returns FALSE

You mean that if you do an var_dump here? You have your data?

PHP Code:

$data['name'] = $this->input->post('name', true);
$data['email'] = $this->input->post('email', true);      
$data['subject'] = $this->input->post('subject', true);      
$data['message'] = $this->input->post('message', true); 
var_dump($data);exit; 


If so, it's your insert model. Not the validation as you said earlier.