Second form on page not performing any action

I have two forms on a page. The first is simply to allow the user to access blocked content. (I understand the risks associated with going this route, but it's just to allow members to view certain information that does not pose any sort of risks).

This is at the top of the page...

<?php
    if (isset($_POST['password']) && $_POST['password'] == 'password') {
        setcookie("password", 'password', strtotime('+1 day'));
        header('Location: index.php');
        exit;
    }
?>
.....
<form method="POST">
   <input type="text" name="password">
   <input type="submit" class="btn btn-full" value="Continue" />
</form>

I believe this is preventing the second form (below) from operating (when you click the submit button, nothing happens. It's as if you hadn't hit the button at all). 

<form action="handler.php" method="post" class="contactForm">
    <div class="form-group">
        <input type="text" name="name" class="form-control" id="name" placeholder="Your Name" data-rule="minlen:4" data-msg="Please enter at least 4 chars" />
        </div>
        <div class="form-group">
                <input type="email" class="form-control" name="email" id="email" placeholder="Your Email" data-rule="email" data-msg="Please enter a valid email" />
        </div>
        <div class="form-group">
                <input type="text" class="form-control" name="subject" id="subject" placeholder="Subject" data-rule="minlen:4" data-msg="Please enter at least 8 chars of subject" />
         </div>
         <div class="form-group">
                <textarea class="form-control" name="message" rows="5" data-rule="required" data-msg="Please write something for us" placeholder="Message"></textarea>
         </div>
    <div class="text-center">
        <input type="submit" value="Send Message" class="btn btn-full" />
    </div>
</form>

What can I do to fix the first part to allow the second form to function?

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