Last I checked scientists were not sure that neurons were the right level at which to understand how our brains think. That is, neurons have microtubule substructures several orders of magnitude smaller than the neurons themselves that may (or may not) have something significant to do with the encoding and processing of information in the brain.

Sure? No. Pretty confident? Yeah. The people who think microtubules and exotic quantum-gravitational effects are critical for intelligence/consciousness are a small minority of (usually) non-neuroscientists who are, in my opinion, allowing some very suspect intuitions to dominate their thinking. I don't have any money right now to propose a bet, but if it turns out that the brain can't be simulated on a sufficient supply of classical hardware, I will boil, shred, and eat my entire (rather expensive) hat.

Consciousness is a much thornier nut to crack. I don't know that anyone has a good handle on that yet.

Daniel Dennet's papers on the subject seem to be making a lot of sense to me. The details are still fuzzy, but I find that having read them, I am less confused on the subject, and I can begin to see how a deterministic system might be designed that would naturally begin to have behavior that would cause them to say the sorts of things about consciousness that I do.