The first question is whether that neural network is learnable. Sure, some configuration of neurons may exist. Is it possible given enough time and space to discover what that configuration is, given a set of inputs and outputs?
The second question is whether "enough time and space" means "beyond the lifetime and resources of anyone alive," in which case it seems perfectly reasonable to me to call it a limitation. I generally want my software to work within my lifetime.
The analogy between deep neural networks and the brain has proven to be very fruitful. Other analogies may as well. See our upcoming paper for more info.
https://grey.colorado.edu/mediawiki/sites/mingus/images/3/3a...
If we use the definition "Aware of its surroundings, responding and acting towards a certain goal" then a lot of things fit that definition.
When an AI plays the atari games, learns from it and plays at a human level, I would call it conscious. It's not a human level conscious agent but conscious nonetheless.
The Computational Cognitive Neuroscience Lab has been studying this topic for decades and has an online textbook here:
http://grey.colorado.edu/CompCogNeuro
The "emergent" deep learning simulator is focused on using these kinds of models to model the brain:
http://grey.colorado.edu/emergent