A child born without senses would really have no cognitive functions whatsoever. I say this because the brain would have absolutely no input on which to calibrate thought.

I possess all five classical senses. I can reproduce any of them as a thought, if I try hard enough, but like most people, I tend to think in sounds or images. But what of a child without senses? If one has lacked vision since birth, can one produce an image in one's head? If one cannot hear, can one think in spoken word? I would imagine not, because the brain has never had input of this type. If you can't hear, then obviously you can't think to yourself in any vocal tongue.

Being only blind and deaf would be a damning burden, but you might still be able to function. Surely there are people in the world who could cope with this and find a way to communicate and share knowledge through the senses of taste, touch, and smell. But what if you then remove these? Now you have a person who cannot see, cannot hear, cannot feel, taste, or smell. What you have here is not a person; he or she is, in essence, a life-sized, anatomically correct and functional doll. The brain is not functioning at all, except to keep the inner workings of the body working.

To answer the question of "What would existence be like for a child born with no senses?", I can only say that it wouldn't be "like" anything. There would be no experiences, no thoughts, no self-awareness. Much as a corpse is no longer the person that once dwelled in it, there would be no "child," just a shell.