Marvin Minsky's theory of a "Society of Mind" describes a (highly) distributed model of the mind. Which BTW, always reminds me of the first Shrek movie, where the donkey jumps up and down, shouting "Take me! Take me!" to Shrek. That's similar to what I observe when I'm undecided but two instances of "sub-processes" (or agents as Minsky calls them) of my mind try to get attention.
Daniel Dennett similarly gives a distributed model of consciousness. Where many parallel "processes" are at work, competing and "observing" each other. And this parallelism is happening with a much, much higher degree than any of our computers parallelism.
All just feelings/vibes unfortunately.
Maybe "Turing machine" is too abstract or simplistic as a concept? Both for real computers and brains?
I can see that a computer is on some level just a lot of sand (silica and metal) but put together in a really complex way, it "suddenly" can add and compare numbers … if we observe the complexity levels from sand to computer and try to see the analogy when comparing cells / neurons to a structure of billions of them somehow interconnected on both a physical and chemical level, evolved during millions of years, I have no problem to accept that brains are still too complex to explain for us.