However, one outside chance of a limit may be that the brain is doing something that is fundamentally different to the kinds of operations carried out by a normal computer - which is essentially the argument in The Emperor's New Mind. When I read that book at the height of my own AI enthusiasm I thought it was pretty silly. However, after reading Anathem (of all things) it made me wonder if perhaps Penrose may have had a point.
So; are you trying to create software that "emulates" human intelligence (i.e. AI)? In which case, yes, software is the major limitation.
Or are you trying to create an artificial (and independently functioning) model of the human brain? In which case you have two limits; hardware speed. But also a huge lack of knowledge about the "secrets" of our brains :)
I suspect #1 will be first solved.
I just don't see much progress on #1 - and people have been trying this approach for 50 years.
Can our thought processes be abstracted into blocks of a few hundred thousand lines of high level language we might actually be capable of writing?
http://www.philosophy.ox.ac.uk/__data/assets/pdf_file/0019/3...
This, of course, has massive ethical and practical implications. It wouldn't be fair to do this without simulating external stimulus (e.g. photo's hitting the back of the eye) or human to human interaction. You wouldn't be able to ask the individual beforehand so it probably would be considered completely unethical... that doesn't mean someone won't do it eventually though.
Even assuming current processing capability growth rates continue, it's unlikely I'll live to see a complete modeling of the human brain (an emulation approach to AI). There's always the possibility someone will discover a secret sauce that permits self-aware artificial intelligence.
That would be an interesting time to live in.