YA: Testing Username/Password Against Database

<?php
$connection = mysql_connect('localhost','root','') or die('Couldn\'t Connect to MySQL: ' . mysql_error();
mysql_select_db("DATABASE_NAME", $connection) or die('Couldn\'t Select Database: ' . mysql_error($connection);
// Because the script will die() if there were errors, no need to check if there were.

// Later on, look into MySQL Injection Protection
$Log_In_Username = $_POST["Log_In_Username"];
$Log_In_Password = $_POST["Log_In_Password"];

$sql = "SELECT Username FROM temp_users WHERE Username='" . $Log_In_Username . "' AND Password='" . $Log_In_Password . "' LIMIT 1"; // I'm assuming you are matching the username and not the email, but I could be wrong. Check for the two conditions, will save you having to compare it later.

$result = mysql_query($sql) or die('Couldn\'t complete Query. Error: ' . mysql_error($connection));

if (mysql_num_rows($result) > 0){
    echo 'Username/Password Combo Match Input';
}else{
    header ("Location: Username_Not_Found.html");
}

?>