I fell asleep at my desk and my head was very close to my laptop - nearly touching - will this damage my brain?

No: Falling asleep on one's cell phone, tablet, or laptop does not cause brain damage if it only happens once. If it happens over and over and over, some sort of damage may occur due to the electromagnetic radiation from these machines. We'll know more about the harmful aspects of these devices after another 1-2 generations (20-50 years). Meanwhile, go to bed before falling asleep elsewhere.