err... the problem isn't "what part does what" it's, how it does it.
Classical computers run through a binary, one input calculation system. Only one input a second and there's only two possible inputs, easy.
Brains however, use chemical neuro-transmitters through millions of interconnected [newly forming] synapses that reach a multitude of brain cells, at the same time. Multiple calculations happening at the same time. Folded in such a way that these calculations are translated into something we can comprehend in a process we still don't truly understand.
We'd need to invent chemical computers if we wanted to realistically simulate the brain, even then it would be amazingly difficult.