I think it should be something like:
<?php
$ParentBread = new WA_MySQLi_RS("ParentBread",$DBConnection,1);
$ParentBread->setQuery("SELECT * FROM productcategories WHERE CategoryPermalink = ?");
$ParentBread->bindParam("s", "".(isset($_GET['parent'])?$_GET['parent']:"") ."", "-1"); //paramPermalink
$ParentBread->execute();
?>