Everything we know about neuroscience has demonstrated that the brain is the sum of the person's thoughts, feelings, memories, ideals, aspirations, etc. Everything that makes you 'you' is controlled by it.
Therefor when the brain dies, not only is the body unable to function, but the person (all those memories, thoughts, feelings, etc) cease to exist as well.
There's another thread on here where people pointed out the exact same thing but somehow it's too difficult a concept for theists to grasp.