Your query isn't executing successfully try this instead:
$user = $_POST['username'];
$check_user = "SELECT username FROM members WHERE username = $user";
$result_user = mysql_query($check_user);
if($result_user) {
$num_rows_user = mysql_num_rows($result_user);
} else {
die($check_user . "<br>" . mysql_errno() . ": " . mysql_error());
}
That will echo out the query and tell you why i'ts failing.