if (isset($_POST['userpassword']))
{
    include('db.php');
    //I have used the name passwordu instead of password in the database as well.
    $query = "SELECT * FROM users WHERE username = '".$_REQUEST['username']."' AND passwordu = '".md5($_REQUEST['userpassword'])."';";
    $result = mysql_query($query);
    if ($result){ //THIS IS WHERE I FEEL THE ERROR IS
        echo "Congratulations. You are now Logged in. You will be logged out when the Browser is closed.";
        $_SESSION['logval'] = TRUE; //Sets the User Logged in for the complete session.
    }
    else echo "Sorry, You Entered Wrong Info.";
}

if ( mysql_num_rows(mysql_query("some query")) == 1 ) { logged in }

... md5($_REQUEST['userpassword'])."';";
                                     ^---this one

$query=<<<HERE
SELECT count(*) as count form users where username=" " and password=" "
HERE;
$send=mysql_query($query);
$row=mysql_fetch_assoc($send);
$count=$row["count"];
if($count=="0"){// not logged in}
else if($count=="1"){//logged in}

$query = "SELECT * FROM users WHERE username = '".$_REQUEST['username']."' AND passwordu = '".md5($_REQUEST['userpassword'])."';";

$query = "SELECT * FROM users WHERE username == '".$_REQUEST['username']."' AND passwordu == '".md5($_REQUEST['userpassword'])."';";

$result = mysql_query($query);

$result = mysql_num_rows(mysql_query($query));