I disagree. The most common definition used by working astrobiologists goes along the line of "chemical system that can self-sustain and can undergo darwinian evolution". Our definition of life is intricately tied with our theories about life's origins, and the counter-examples to that definition are fictional and their premise falls apart on closer examination.
Let's take the self-aware computer you mentioned. How would such a computer come to being, exactly? It could have been built by something that does satisfy the above definition (in which case you could consider the computer not alive, but a biosignature). Or it could have been built through some darwinian process, and you're still firmly within the above definition.
Steve Benner has a nice paper about this. DOI: 10.1089/ast.2010.0524
The article doesn't actually address the problems with the 'evolutionary definition', probably because it would mean trying to chip away at a theory that a lot of people spent a lot of time trying to disprove.
> Alive are the things we say are alive, which is mostly stuff like us: some type of metabolism, growth, response to stimuli. By that definition we would certainly recognize it, at least up close.
What about fire?