Problem with my script

Below is a login script that i made. Everything works fine when the script encounters errors in the form, but when I actually do type in the correct username and password, nothing shows up. Hope somebody can point out whats wrong. I intentionally deleted the db user and pass, so don’t worry about that.


<?php

//Database connection
function db_connect(){
	$dbHost = "localhost";
	$dbUser = "";
	$dbPass = "";
	$dbName = "";

	$conn = mysql_pconnect($dbHost, $dbUser, $dbPass);
	if(!$conn)
	{
		echo"No connection";
		return 0;
	}

	if(!mysql_select_db($dbName, $conn))
	{
		echo"No db";
		return 0;
	}
	return 1;
}

//checks username and password in database
function login($username, $password){
	
	$conn = db_connect();

	if(!$conn){
		echo"can't connect";
		return 0;
	}

	$query = "SELECT * from users
		  WHERE username = '$username'
		  AND user_password = md5('$password')";

	$result = mysql_query($query);

	if(!$result){
		echo"Can't run query, try again later";
		return 0;
	}

	if(mysql_num_rows($result)>0)
		return 1;

	else	
		return 0;
}

//Checks if form has been filled
function filled_out($form_vars){
	foreach($form_vars as $key => $value){
		if(!isset($key) || ($value == ''))
			return 0;
	}
	
	return 1;
}

function Login_User(){
	global $_SESSION;
	global $username, $password, $Submit;
	if(isset($_POST['Submit']))
	{
		$username = $_POST['username'];
		$passwd = $_POST['password'];
		if(!filled_out($_POST))
		{
			echo"You did not fill out all the fields";
			LoginForm();
			exit;
		}
		
		if(login($username, $passwd))
		{
			$_SESSION['valid_user'] = $username;
			exit;
		}
		
		else
		{
			echo"The username and password you supplied are incorrect";
			LoginForm();
			exit;
		}
		
	}

else
	LoginForm();		
}

//Displays the form
function LoginForm(){
	global $PHP_SELF;
	global $username, $password;
	global $action;
	?>
<form method="POST" action="<? echo $PHP_SELF ?>">
  <table width="252" border="0" align="center" cellpadding="0" cellspacing="0">
    <tr> 
      <td colspan="2"> <div align="left"><font face='Verdana' size='1'><b>Username:</b></font></div></td>
      <td colspan="2"> <div align="left">
          <input name="username" type="text" value="<?php echo $username?>">
        </div></td>
    </tr>
    <tr> 
      <td colspan="2"><div align="left"><font face='Verdana' size='1'><b>Password:</b></span></font></div></td>
      <td colspan="2"> <div align="left"> 
          <input name="password" type="password" id="password">
        </div></td>
    </tr>
    <tr> 
      <td colspan="4"></td>
    </tr>
    <tr> 
      <td colspan="4">&nbsp;</td>
    </tr>
    <tr> 
      <td colspan="4"><div align="center"> 
          <input name="Submit" type="Submit" value="Login">
        </div></td>
    </tr>
  </table>
</form>
<?
}

//Program starts here

session_start();


if(isset($_SESSION['valid_user']))
{
	echo"<center>Access Granted</center>";	
}

else
{
	Login_User();	
}

?>