Just took a quick look at my old 1.6ST install and it does not appear that clients can ever select department. Only Staff can. That being said there was a mod that allowed auto assignment:
http://osticket.com/forums/showthread.php?t=4311&highlight=assign(http://osticket.com/forums/showthread.php?t=4311&highlight=assign)
1.7ST also does not appear to allow the client (ticket opener) to pick their own department. But 1.7ST has ticket filters also and can assign them to departments.
Side note: you should really consider upgrading to 1.7ST.