Quite contrary to solipsism, I'd posit that what matters is behaviour. If a cognitive process is able to communicate with us and convincingly recount its reflections about itself, for all intents and purposes that system is conscious. It doesn't matter if it differs from our consciousness in significant ways.
Let's consider a machine that is able to reflect on itself quote effectively but it's also to turn on and off that module "at will". This is quite different from our experience of consciousness, in that we're not able to turn off our own consciousness, to the extent that we believe we're "there" only while we're conscious of it, and thus we end up equating our existence with those surface experiences. But we're way more than that. Were made of a thousand brains and not all processing reaches what we call our consciousness.
A system that exhibits a different mixture of those mechanism shouldn't be ruled out as not meeting the arbitrarily anthropomorphic bar of consciousness.
Unfortunately this definition doesn't help weeding out misconceptions such as philosophical zombies. All you have to do is to say that a system may claim it's conscious without really being "aware" of it's own existence. This definition doesn't help because it doesn't say what being aware of it's own existence mean, offering arguably a circular definition.