Your sensory system is still running

There are brain subsystems that are still running, but they are not necessarily ones "you" identify with. If you replaced the parts/networks of the brain that control your heart and lungs (through some molecular nanotechnology), would "you" still be you? My intuition says yes. The fact that "something is running" doesn't mean that something is you.

I know the computer metaphor doesn't work well for the brain, but imagine the system in the brain that wakes you up when you hear some sound could be sort of like when a sleeping computer that gets woken up by a signal in the computer network.

Also as others have mentioned, I'm pretty sure during anesthesia/coma there can be periods where you are completely lacking any experience.