I like to think of complex problems like these. So far, I think that conscience as we know it exists purely due to the activity of the brain. That's the scientific approach. However, there are several major caveats, going into metaphysics. First, supernatural occurences such as the "souls of the dead" "speaking" to mediums - sure, not documented or scientifically proven, but a possibility nonetheless. Second, some notable occurences of - again, unproven - transplant memory. And finally, the theory of reincarnation. All of these tie into the concept of the human soul. Evidently, the soul is some form of an integral information field - quite possibly an imprint of structured information created by the human brain and its activity. And then we circle back from metaphysics into physics - for an imprint of information to be conceivable, much less analyzeable or transferrable, information must exist in the universe as a form of energy. (Which leads straight into a work of Stanislaw Lem that mentions Donda's Law - that information, or structured collection of matter, has its own mass. It's impossibly small, yet in the age of computers it is possible to gather enough information to notice the mass.) It is possible that the Earth has accumulated a sort of a "psychosphere", a collection of imprints of people that have lived on it, and that these imprints periodically manifest as "speaking dead" or even ghosts. The idea that an information imprint may continue to exist or function when the biological machine that created it has been destroyed gives a different meaning to Heaven or Hell - they may as well be literal, as the magnetic fields surrounding the Earth would have an effect on the imprints, and the structure and integrity of the imprints could both affect the exact conditions they would be put into.
Alright, that went quite a bit too far beyond the scope of any sort of normal science or theology. Feel free to discuss.