It would be very helpful it you could add the database layouts.

Also, you only reference one database but you state we need to pull information from two.

In your class you state:
var $cat_id;
var $depth;
var $cat_title;
var $cat_parent_id;
var $cat_long_title;

It is hard to know which tables these belong to.
Also, in your $db->fetchrow(), is this a mysql_fetch_row, or mysql_fetch_object, assoc? Assuming you said row, im guessing it would be a fetch row, but clarification would be nice. Also, maybe a working script.