"well, computers have rules they have to follow"
Just like human brains. In the case of brains it's a set of biological (genetic, chemical, physical, etc.) rules. Those rules can be 'emulated' or even 'simulated' in a 'normal' computer. The 'entity' resulting from such a simulation should show the same kind of behaviour as a human brain.
"there are things that you can say about the system that you cannot prove within that system. In particular, the statement "this system is consistent" is one of them."
That's true both for human brains and for computers. No human brain can say about itself 'this system is consistent' without lots of external data. Actually, no human KNOWS whether human brains are consistent or not. :-)