Although the question itself is rather vague, the promise of enquiry, speculation and interrogation you have raised is fascinating, and one in which will often hang on perspectives and the drifting of one's own inquirying pursuits.

With that said, you could focus your question by going through this entry: http://plato.stanford.edu/entries/existence/, and if that hasn't sparked an interest, that is, if your question pertains more to notions we have of I, mind, identity, ego, self etc why not have a look at Hume's bundle theory, the Buddhist's conception of skandhas, Nagarjuna's critique of svabhāva, Heidegger's Das Man (sections 25-32 of B&T, not just some wiki entry), Freud's reality principle and ego, Searles & Dreyfus' essays on intentionality, and that kind of thing.

Of course not. I wouldn't be able to prove anything if I did not first exist.

to prove non-existence, don't we need to know the definition of existence?

I don't think I exist,
I am compiled of atoms, as is everything else.
All atom is compiled of 11 (or 26) dimensional energy strings. So everything in this world is just energy. To make a distinction between one group of energy from another is like standing on a beach, pointing to the general left side of the ocean saying, "that's john", moving your finger a inch to the right and saying, "over there is jessica", pointing your finger a little downwards, "over there is the market". To others, it's just ocean...
Does the ocean exist? yes. Does John, jessica and the market exist? apparently. Can you differentiate them? no.

The only way to prove the non-existence of something is to show that its existence would be contradictory. This could involve either showing that the predicates it instantiates are mutually contradictory (for example, that it is square and circular, assuming that all squares are not circular and all circles are not square) or that it instantiates a predicate which is already shown to not be instantiated. But the latter involves already having a proof of something's non-existence.

So the simple answer is this: if someone can show that their existence is contradictory, then yes. But assuming that a contradictory existence is impossible, they would not be around to prove it in the first place, so I don't think that anyone can show that their existence is contradictory. So no.

To say that we exist as atoms is not a medical fact. We continually take in atoms that are not part of our physical body that enter into reactions and are used to repair cells that continually need repair. Our body has an external skin that is composed of 3 layers: Epidermis, Dermis, and Hypodermis. The outer layer wears off, the middle layer becomes the top layer, and the bottom layer becomes the middle layer. It takes 30 days for every layer and every atom to become non body and new cells take their place. Even our bones are fluid. Medical scientists state that every atom in our body is completely replaced by atoms from outside our physical body every 7 years. If you or I were our physical body that is composed with atoms, we would be a completely self every 7 years. Since I am the same self that I have always been, I cannot be the physical body that is composed by atoms.

unconsciousness is a form of nonexistence. so long as we are unconscious, then we do not exist to ourselves.

there is an other thing to understand that there is an other thing in our bodies which is can't be seen but it may be done of scientists more effort for it and it thing help mind to control all the body we can also say that it's a connective helper !

Humans actually use energy to live. Therefore we cannot be energy.

We always knew we are a spirit placed into a lower organic life form that exists. And we all know that we only exist by the consuming of food and water.

Both bodies that we consume are bio organic. Therefore we state we live in a life of balances.

Light is a product of gases burning which water/oxygen cool. Energy is already being consumed to produce light.

Not while your are existing no...

This makes sense. It isn't that we are not comprised of atoms; even if specific atoms come to be revised, at any point in time atoms do make up our physical presence. But our existence also comprises what we do physically, sensory input that contributes toward that, thoughts, etc. Atoms are only part of all this.

Moreover, one's existence is, somehow, wrapped up with consciousness, too. It's an open question whether consciousness is a product of activity, say, in a certain segment of the brain (human brain only? [but not newborn babies?] pet dog's brain? mosquito brain?) or whether consciousness is a more universal entity endemic in -- according to some theories -- everything.

"Not while your are existing no..."

But, then, a related question: could it be proved that anyone does not exist, or did never exist? (I omit "will exist" -- why do I do that?)