The brain is like a radio. A single human consciousness (a.k.a. a soul) is far too vast and complex to exist in a three pound blob of grey goo. The size of the actual hardware on which we each run is unknown but can be assumed to be enormous.
That soul machine communicates with its dedicated brain through something like radio waves but the nature of those "thought waves" only interacts with our reality within brains. Thought waves are therefore invisible to scientific observation since the only scientists who even see them are neurologists who are so dedicated to proving that the brain is the source of consciousness, that they consider any alternative explanation to be religious/superstitious nonsense.
What processing power is actually resident in the brain is mostly dedicated to encryption, ensuring privacy between each soul and its body.
The brain is therefore a two-directional radio transceiver, constantly connecting the corporeal avatars (which we call bodies) to the soul which resides in an elsewhere far beyond.
As for disembodied souls not being able to think, this could be a matter of context. A soul may be capable of an enormous spectrum of consciousness, but the aspect of that capability which we call thought, the aspect which has context for a linear corporeal reality, requires a connection to that reality. Without the brain, the soul has no understanding of time or causality, so the way that it functions when not attached to a brain cannot be recognized as identity or memory or thought. It still is and still functions on many levels, but none of those remaining levels is anything like what we perceive as life.