I believe that the "Hard Problem of Consciousness" will be solved by conceptual advances made in connection with cognitive neuroscience. Let me explain. No one has a clue (at the moment) how to answer the question of why the neural basis of the phenomenal feel of my experience of red is the neural basis of that phenomenal feel rather than a different one or none at all. There is an "explanatory gap" here which no one has a clue how to close.
This problem is conceptually and explanatorily prior to the issue of what the nature of the self is, as can be seen in part by noting that the problem would persist even for experiences that are not organized into selves. No doubt closing the explanatory gap will require ideas that we cannot now anticipate. The mind-body problem is so singular that no appeal to the closing of past explanatory gaps really justifies optimism, but I am optimistic nonetheless.