I am having this problem as well. I received it torn apart with a broken hard drive. I replaced the hard drive and did a restore, and the click wheel and buttons don't work. I replaced the logic board thinking that was the problem, but that didn't fix anything. The hold switch isn't the problem because the icon will go away.
I believe that this is actually a scroll wheel problem, and would be a simple fix. I am waiting on a new one, and will respond with the results.
- The new scroll wheel fixed the problem. I tried a 5th gen scroll wheel, and that didn't work. There must be something unique about the classic's wheel.