Try this. Suppose everything that is explained is explained by facts about the physical world - that's physicalism. If zombies were possible and existed, we would be physically indistinguishable from them. But they would have no consciousness. So whatever explains our consciousness cannot be physical. If it were, it would also make consciousness for the zombies. That's the point of the physical indistinguishability between us and the zombies. There is a very good article in the Stanford Encyclopedia of Philosophy called "Zombies", by Robert Kirk, by the way, which will clear everything up for you.
Louise Anthony's reply is absolutely right, though the problem of other minds will be always with us no doubt. I wonder whether there is something else in addition in your mind that lies behind the question. Are you suggesting that whenever I am conscious there is a very interesting cause in the external world - the consciousness of others? So, for example, when I catch someone's eye, or when I become aware of the intelligence embodied in the design of a building, I become conscious. I think that there is truth to this interesting empirical proposal, but I wonder whether what is happening is that I become more conscious than I was in these cases, or conscious in a new way. A certain amount of education involves this, and, as Nagel pointed out a long time ago, the consciousness of mutual desire does too. But presumably there has to be a basis of consciousness already, or I could not become aware of anything conscious tugging at me from the external world. There has to be a consciousness there to be snagged by another consciousness. Babies do respond to consciousness in their environment, and grow and socialize with it, but presumably in their development the growth to consciousness would happen without the stimuli offered by other human beings, though perhaps in a different way.
There are lots of things that don't exist that we can conceive of, most obviously fictional characters and objects, though our conceptions of them may be less detailed or thorough-going than our conceptions of things that do exist. (They may also be more detailed. We may know more about the characters in Tolstoy's novels than about some real people.) We can conceive of an elixir of youth, though there may not be such a thing, for example. And if consciousness exists, where does it go when you are meditating or fast asleep? Well, why does it have to go anywhere? Isn't it more like a noise, say, that is real enough in its way, but which just shuts down or disappears when the thing making it go stops, and doesn't have to go anywhere? Of course if the individual consciousness is a sort of stuff, rather than a kind of attention, a substance even, in the philosophical sense, then presumably it keeps on going even if it isn't with you any more. But it is difficult to see how that would work; what happens to your consciousness if it continues to exist but you are not conscious of it? It is hard to say, as Aristotle would say! On the other hand it is easy enough to see how you can go on with or without consciousness. It happens to me every day.
My little toe is conscious, and it is a part of me, perhaps even a "constituent" part. I put in the scare quotes because I am wondering whether "constituent" means "essential"; if it does my big toe is not a constituent part of me. But if "A is a constituent of B" means "A is part of B", then my big toe is a constituent part of me, but the phrase "constituent part" is a tautology - it says that same thing twice. Are there parts of me which are not constituent parts, but some other kind?
You can imagine after surgery a doctor asking, "Is your little toe conscious?", and the answer might be "Yes", and working through to the big toe; the answer then might be, "No".
It is not at all obvious why we should feel the Cartesian tug to say that it is I, not my big toe, that is conscious, except for dubious epistemological reasons such as that we can imagine the consciousness without the toe. The same seems to be true of my psychological parts in Descartes' sense in the Meditations. My thinking might be highly conscious, my feelings almost or completely unconscious, perhaps to my detriment, or the other way round. Is there any reason beyond a fondness for the unity of panpsychism (everything is more or less conscious) to suppose that individual cells might be? You might suppose that my armchair is conscious, but there is no special reason to think so, whereas there is for my cat. Cells don't seem to have the psychological activity usually associated with consciousness.
Naturally my little toe is not a person (or a "self") but why should that prevent it from being conscious? Wasn't that Descartes' mistake?
Why should the possession of intelligence (whatever we mean by this, but say it means winning chess games against the world chess champion, winning bridge games with bad partners against the world bridge champions, issuing correct diagnoses for car repairs, predicting stock market fluctuations, analyzing individual psychology, and so on) require consciousness? We know that when Kasparov played Deep Blue he "sensed" a "weird" and "alien" kind of consciousness - or said and thought he did. I have the same thing with my very complicated telephone handset - it is against me, spitefully, deliberately and consciously. If we allow that playing chess well involves intelligence, then Deep Blue or Deep Fritz or Shredder show the following thing: intelligence does not require consciousness. If we deny consciousness to the systems, then your question does not arise at all, because (a) is false. (I have used "consciousness", but "self-awareness" implies much more, including I think the critique of elements of behaviour.)