I think the most likely way to achieve a "real" general intelligence will be by reverse engineering how functioning brains and minds work. At least is an area where continual, albeit rather slow, progress is being made - eventually we will know how the mind works (assuming that there isn't anything fundamentally weird going on - which seems unlikely).
Once we understand how minds actually work I suspect there should be a good chance that we can upgrade/optimize these structures - either by architectural improvements or by throwing more resources at the areas that constrain current performance in biological brains. At that point things really could get rather exciting - but I don't expect this to happen in my lifetime (I'm in my 40s).