I think you have probably done enough to show there is something wrong. One interesting question: are the sprocket and hub rotating at the same speed? If so, it might be an indication that the mechanism has seized. In any case, your next step should probably be to clean and re-lubricate. I think there are descriptions on the web of how to do that without buying Shimano's special-purpose oil. That would probably be the best next step even if it seemed to be working ...