Update if variables exist else echo an error message?

Update if variables exist else echo an error message?

How can I make this script to where if it finds that the fname and lname
do not exist that it will pop up a message saying that they never signed
in.
<?php
session_start();
include_once("connect.php");
date_default_timezone_set("America/Winnipeg");
$date = ("m-d-Y");
$timeout = date("g:i:s a");
if ("SELECT EXISTS(SELECT * FROM signin_out WHERE
lname='".$_POST['lastname']."' AND
fname='".$_POST['firstname']."'
AND date='".$date."')") {
mysql_query("UPDATE signin_out SET timeout='" . $timeout . "'
WHERE lname='" . $_POST['lastname'] . "' AND fname='" .
$_POST['firstname'] . "' AND timeout='' ");
header("Location: ../index.html");
} else {
echo "<script type='text/javascript>'";
echo "alert('<p>Oops! You never signed in!</p><br><p>Please contact a
Librarian</p>');'";
echo "</script>'";
header('Location: ../index.php?notsignedin');
}
?>
This is an intranet site for a highschool.