Using "and" in SQL is actually the word AND, not &&. Also, using or die() on your $Query variable isn't doing any good, becuase it is just a string. And the query function is mysql_query, not mysql_db_query, so...
// Change
$Query = "SELECT * FROM members WHERE username='$username' && password='$password'" or die (mysql_error());
$Result = mysql_db_query ("idealgr_orders", $Query, $dbh) or die (mysql_error());
// To
$Query = "SELECT * FROM members
WHERE username='".$username."'
AND password='".$password."'";
$Result = mysql_query($Query) or die("ERROR: ".mysql_error());