Well if you think about it, it'd be relatively simple to replace the click wheel, compared to trying the motherboard, so you should find a cheap click wheel on ebay, and use [http://www.ifixit.com/Guide/Repair/Installing-iPod-Nano-4th-Generation-Click-Wheel/1160/1|this guide] to install it. If that doesn't work then it's probably the logic board.
Does it physically work though, or does it just not register?