If the connection is not loose, the center button part of the clickwheel is most likely broken. Although there is no specific repair guide to replace the clickwheel on this iPod, if you follow the repair guide for replacing the screen and then the teardown guide for how the clickwheel assembly is attached, you should have no problem replacing said clickwheel.
I just finished such a repair myself, and was able to replace the clickwheel without any problems whatsoever. However, as the guides state, getting new iPod back plate is recommended, as taking it off takes patience, and the first time you attempt to remove it you will probably bend it (as I did).
Best of luck!