A brain can certainly memorize and follow a fixed set of rules to update the tape on a Turing machine. Therefore the brain is at least a Universal Computer. Furthermore there is nothing in the domain of sensory-motor tasks that is in principle beyond computer controlled robotics. So then praytell, what can a brain do that a computer can't?

Careful. The current answers to that question live on a small island that's been eroding at an alarming pace. Some project that the island will be totally washed away in our lifetime. You sure you want to build there?