Logic Pro,
I have had this problem about a few months ago, it started happening right after I opened my iPod ( and didn`t close it back together properly ). I have a hunch, that if the back case & the aluminum frame are not connected to the boards GND or - they cause the iPod to function this way. At your own risk, you can try to open it up. The only thing I have seen coming directly from the clickwheel assembly, is a small ribbon, that has an exposed portion of metal, that is pressed to the frame, in the middle-left side of the iPod. See if that`s properly connected, also, you might want to clean it up ( especially the back part ) CAREFULLY ( there might be fine dust/fibres preventing everything from making a good connection ).
!PS!: Be careful ... take extra time in disconnecting every single connector when pooping up back.
Good Luck, Darie