эта форма выдает ошибку «НЕ ОТПРАВЛЕНО»

Изменить форму action="$_SELF" на action="$_SERVER['PHP_SELF']", потому что не существует константы, как $_SELF.

На самом деле его работа здесь без ошибок, попробуйте с этим маленьким скриптом, проверить или отправить по электронной почте:

<?php
$to = "[email protected]";
$subject = "My subject";
$txt = "Hello world!";
$headers = "From: [email protected]" . "\r\n" .
"CC: [email protected]";

mail($to,$subject,$txt,$headers);
?>

Я проверил ваш скрипт с небольшой настройкой:

<form id="contactform" method="post" action="#">
        <label class="hide" for="author">Full Name</label> 
        <input class="input-fields" id="author" name="name" type="text" placeholder="Full Name" value="aaa" required autofocus />

        <label class="hide" for="email">Email</label> 
        <input class="input-fields" id="email" name="email" type="text" placeholder="Email Address" value="[email protected]" autofocus />

        <label class="hide" for="email">Mobile No</label> 
        <input class="input-fields" id="email" name="phone_no" type="text" placeholder="Mobile No" value="0322233355" autofocus />

        <label class="hide" for="author">Company</label> 
        <input class="input-fields" id="author" name="company" type="text" placeholder="Company" value="aaa" required autofocus />

        <label class="hide" for="select_category">Select a Industry:</label> 
        <span id="select_group" class="select-group">
            <select name="vehicle">
                <option value="General" >Select a Industry:</option>
                <option value="General" >Health Centres Hospitals</option>
                <option value="Sales" >Tradeshows Conferences</option>
                <option value="Support" >Fast Foods and Restaurants</option>
                <option value="Support" >Night CLub, Bars and Disos</option>
                <option value="Support" >Banks , Rent Estate</option>
                <option value="Support" >Educational Institute</option>
                <option value="Support" >Recreational Facilities</option>
                <option value="Support" >Malls,Luxury Retail and Store Windows</option>
            </select>
        </span>

        <label class="hide" for="subject_title">Solutions</label> 
        <input class="input-fields" id="subject_title" name="solution" type="text" placeholder="Solutions" value="aaa" autofocus />

        <label class="hide" for="author">Require</label> 
        <input class="input-fields" id="author" name="require" type="text" placeholder="Require" value="aaa" required autofocus />

        <label class="hide" for="comment">Message</label> 
        <textarea id="comment" class="input-fields" placeholder="Message" name="message" cols="40" rows="20"></textarea>
        <span class="form_response">
                                           <ul id="errors" class="">
                                                    <li id="info">There were some problems with your form submission:</li>
                                           </ul>
                                                <p id="success" class="">Thanks for your message! We will get back to you ASAP!</p>
                                    </span>
        <input name="submit" type="submit" id="submit-contact-info" class="contact-info-submit form-submit-button span2" value="Send message">
                </form>
                          </div>
                </div>
            </article>
        </main>
  </div>


 <?php
         //If the form is submitted

           if(isset($_REQUEST['submit'])) 
           {
             $message = $_POST['message'];
           }                                     
                   //Check to make sure that the exit date field is not empty
             if(trim($_POST['vehicle']) == '') {
               $hasError = "1";
             } else {
               $vehicle = trim($_POST['vehicle']);
             }
         //Check to make sure that the exit date field is not empty
             if(trim($_POST['require']) == '') {
               $hasError = "2";
             } else {
               $require = trim($_POST['require']);
             }
         //Check to make sure that the exit date field is not empty
             if(trim($_POST['solution']) == '') {
               $hasError = "3";
             } else {
               $solution = trim($_POST['solution']);
             }

           //Check to make sure that the name field is not empty
             if(trim($_POST['name']) == '') {
               $hasError = "4";
             } else {
               $name = trim($_POST['name']);
             }

           //Check to make sure sure that a valid email address is submitted
             if(trim($_POST['email']) == '')  {
               $hasError = "5";
             } else if (!eregi("^[A-Z0-9._%-]+@[A-Z0-9._%-]+\.[A-Z]{2,4}$", trim($_POST['email']))) {
               $hasError = "6";
             } else {
               $email = trim($_POST['email']);
             }
           //Check to make sure that the mobile no field is not empty
             if(trim($_POST['phone_no']) == '') {
               $hasError = "7";
             } else {
               $phone_no = trim($_POST['phone_no']);
             }

             //If there is no error, send the email
    if(!isset($hasError)) 
      {
      echo "OK";
               $emailTo = "[email protected]"; //Put your own email address here
               $body = "Name: $name \n\nEmail: $email \n\nMobile No: $phone_no \n\n Your Industry: $vehicle \n\
              \n\n Your Requirement: $require \n\n Your Solution: $solution \n\n 
              \n\n Message : $message 
              \n\nPlease Contact $name  on $phone_no\n \n /====================================/ ";
               $headers = 'From: Touch Active  <'. $emailTo .'>' . "\r\n" . 'Reply-To: ' . $email; 


                                              if(mail($emailTo, 'Mail From Touch Active', $body, $headers))
                                              { //Replace Your Website Subject
                                                $response=1;
                                                $emailSent = true; 


                                              ?> 

               <div id="responsive-container" ><p>Thanks For Messaging Us You Will Shortly Expect Our Assistance ( With In 24hrs ).</p></div>

               <?php
               }
                else
               {
                 ?>
                 <div id="page-title"><h2>Failed To Sent</h2></div>
                 <?php echo "NOK";
                 echo $hasError;
                 echo $response;
                 $response=0;
               }
         }
         else{
         echo $hasError;
         }

   ?>