Why does this NOR operator in PHP not working?

I am trying to create a signup page on my website, and I have all of the filtering code done. So what I am trying to do in the following code is to make sure the username doesn't already exist in the database and proceed from there. The problem is this: I am doing a NOR operator with $error and $captchaError but even though when I print them, the values of both of them are false, the code in the if statement doesn't end up running and I seriously can't understand why. Here's the code:

<?php
    $error = false;
    $captchaError = false;
    if($_POST) {
        $username = $_POST["username"];
        if (!preg_match("/^[0-9A-Za-z_]{3,16}+$/", $username)) {
            $error = true;
        }
        $email = $_POST["email"];
        if (!filter_var($email, FILTER_VALIDATE_EMAIL) || strlen($email) > 50) {
            $error = true;
        }
        $password = $_POST["password"];
        if(!preg_match("/^[-0-9A-Za-z!@#$%^&*_+=]{6,}+$/", $password)) {
            $error = true;
        }
        $captcha = $_POST['g-recaptcha-response'];
        $response = json_decode(file_get_contents("http://ift.tt/29iRz02".$captcha."&remoteip=".$_SERVER['REMOTE_ADDR']), true);
        if(!$captcha || $response['success'] == false) {
            $captchaError = true;
        }
        if((!$error) && (!captchaError)) {
            include("../res/db.php");
            $prep = $conn->prepare("SELECT * FROM users WHERE name=?");
            $prep->bind_param("s", $username);
            $prep->execute();
            $prep->store_result();
            echo "why doesn't this run??";
            var_dump($prep->num_rows);
        }
    }
?>

And this is the form:

<form method="POST" action="">
    <?php if($error) { echo "<p class=\"text-danger text-center\">Error: Something went wrong while submitting your form</p>";}?>
    <div class="form-group">
        <h2 class="text-center">Username </h2>
        <input value="<?php if($captchaError) {echo $username;}?>" class="form-control input-lg" pattern="[0-9A-Za-z_]{3,16}" title="You must use between 3 and 16 legal characters (0-9,a-z,A-Z and _)" type="text" name="username" maxlength="16" required>
    </div>
    <div class="form-group">
        <h2 class="text-center">Email</h2>
        <input value="<?php if($captchaError) {echo $email;}?>" class="form-control input-lg" type="email" name="email" maxlength="50" required>
    </div>
    <div class="form-group">
        <h2 class="text-center">Password</h2>
        <input class="form-control input-lg" type="password" name="password" pattern="[-0-9A-Za-z!@#$%^&*_+=]{6,}" title="You must use more than 6 legal characters (0-9,a-z,A-Z and !@#$%^&*_-+=)" required>
    </div>
    <div class="text-center">
        <?php if($captchaError) { echo "<p class=\"text-danger text-center\">Error: You must fill out the captcha</p>";}?>
        <div class="g-recaptcha" data-sitekey="{MYPUBLICKEY}"></div>
    </div>
    <div class="text-center">
        <button type="submit" class="btn btn-primary btn-lg">Submit</button>
    </div>
</form>

Remember, whenever I print the values of $error and $captchaError they are both false, which should make the if statement run, but for some reason it doesn't, why?