Human consciousness has logically to be a product of the physical structure of human beings.
So we genuinely cannot even begin to guess as to what actually imbues consciousness into our neural processes. It could be anything from "it's actually just the physical processes" through "there's a soul piloting our brains by influencing quantum noise" to "the brain is basically an antenna for our metaphysical self and death/disability is the loss of connection"
Unless we obtain any evidence whatsoever that this can't be the case, Occam's razor would suggest that this is the hypothesis to explore, without looking for new physics or other unlikely assumptions.
Are we more than biological "computers"?
I think we are complex biological systems that we do not fully understand yet but that does not mean anything supernatural or beyond our understanding of physics is at play.