Technically, I don't consider myself an atheist, but I believe that the lights would go out as you surmised for atheists. As OCD said, your earliest memories usually begin once you begin to develop language skills, so once my brain is disconnected from my subconscious, how could it survive. Sensory functions are controlled by the brain, nerves and our bodies and although there may be some sort of matter that survives, I've always thought of it as becoming scattered and blended with matter in the environment. That's where I like to think the human connection comes in; we all contain part of this DNA/matter/collective consciousness.
At one point, I did believe in a Hindu-type of caste system (that's what I think I remember it to be) where your soul would return continually until you became capable of reaching nirvana, but now find it difficult to believe that my soul or consciousness could instantaneously transport to another being. Even if that were so, what would have happened to my memories and baggage?
I wish I knew more about DNA, though. Somehow, I wonder if DNA transplantation (not necessarily cloning) would accomplish this, enabling the soul or consciousness to live on. Somehow I think it may tie in with all that DNA out there floating around when we die.