Sorry for such a basic question, but why is this nested conditional not working?!

If $new_cust is FALSE then the code goes to the hightlighted red code below which is clearly wrong.

Code:
  if (isset($submitted)) {
    // Handle the form.
    if ($new_cust == TRUE) {
      // For New Customers
      if(empty($email)) {
        $errors['email']='Please enter a valid E-mail address.';
      };
    } else {
      // For Existing Customers
      if(empty($email)) {
        $errors['email']='Please enter a valid E-mail address.';
      };

      if(empty($password1)) {
        $errors['password1']='Please enter your Password valid E-mail address.';
      };
    }
  }

Amy