First of all, this isn't really a "proof," it is merely an argument. And despite Descartes's unquestionable greatness, this particular argument has not aged well.

>Possibly, the most logically sound proof I have encountered,
>as follows;

Go read some Euclid. Or better yet, Hilbert or Bertrand Russell. Just an aside.

>First, Descartes must prove that he himself exists, and he
>does so through his famous statement, "I think therefore I
>am", as it is a clear and distinct statement that is self
>evident, no proof beyond the act of saying it is required.

Well, that's a question of epistemology, not a tenet of logic.

>The reasoning behind this statement is as follows; if I am
>able to percieve my own existence from within, I must
>therefore exist.

And that's not reasoning, it's just repetition.

>Next, Descartes will discuss the relationship between
>physical objects, and himself. He is not certain of physical
>objects in his environment, but of his relationship to them.

And that much is very commendable. Descartes's relationalism is probably his greatest achievement, though it is still disputed today, in some quarters (I sit solidly on his side, though).

>In an experiment, Descartes takes a piece of wax, and allows
>it to melt. He then, observes what has changed, and what has
>not changed. Through his experiment, Descartes arrives at
>the conclusion that the wax, may melt in many different
>ways, or in inifinite ways. The state of change between a
>solid piece of wax and a melted piece of wax is infinite. A
>simple example of the infinite are numbers.

And here's where the age of the argument really begins to drag it down. In his time, it was natural to assume that the number, N, of ways in which a block of wax could melt is infinite. In fact, it is now known physically that N is not infinite! It is an enormous number, but finite nonetheless. This fact is a simple result of modern quantum mechanics, and it underlies all of our understanding of statistical thermodynamics. This is not to say that we "know" N is finite. There are likely some errors in the present formulation of quantum theory. Nonetheless, it is far more reasonable for us to assume N is finite.

But Descartes's argument is not about wax. It's about the nature of infinity in the physical world. In fact many of the quantities of the physical world, once assumed to be infinite, have been rendered finite by the modern quantum viewpoint. The extent of this is not yet completely clear. Many quantum systems admit finite bases (that is, a finite number of "states"). Many more admit "countable" bases (that's a designation that might be considered "in between" the standard definitions of finite and infinite), and some, truly, uncountably infinite bases. In fact, most systems admit more than one of the above, simultaneously. That is, the question of how many states a system might take, depends on how the observer chooses to differentiate them. And in fact, in the most mathematically rigorous treatments of quantum theory yet made, uncountably infinite bases are avoided like the plague. The problem is that they usually lead to logical inconsistencies, a sign that the "methods of distinction" which lead to infinite bases are generally unnatural, and amount to the philosopher forcing too much of his own opinions upon the system.

I doubt I'm making any sense. My point is that it now appears unlikely that any physical phenomena permit truly infinite variation. It seems more likely that the concept of infinity is an invention of man, and is forced upon the physical world now far too quickly.

>I am not detailing each point of study as I want to arrive
>at the proof of God as quickly as possible for the sake of
>this conversation, so please excuse me for leaving
>information out if you have already studied Descartes.
>
>Next, Descartes invents the idea of the "Evil Genius" which
>may be percieved as something that is decieving to his
>senses and himself. In order to disprove the existence of
>the "Evil Genius", Descartes is faced with the challenge of
>proving God's existence. He does this as follows;
>
>Human beings are finite beings, meaning, our physical bodies
>will eventually die.

Sure.

>Also, as finite beings, we are
>incapable of the infinite, yet we can be certain the
>infinite exists by observing a melting a piece of wax.

Again, that's not really true. We ASSUME the infinite exists, or rather, Descartes did.

>We
>can grasp the concept of the infinite, but we are incapable
>of it's excecution.

That seems to me to be a sign that it was a figment of our imagination all along.

>If you feel otherwise, please state how
>as human beings, we can excecute the infinite. Descartes
>concludes that God is a supreme being capable of the
>infinite.

And this is a HUGE leap! Even if we were to assume the physical existence of the infinite, there is absolutely no reason this requires a "being capable of the infinite."

>Do you find this to be sound proof for the existence of God
>that is clear and distinct?

Well, I think my view is clear.

>Furthermore, Descartes explores free will. Thus far, he is
>certain of Himself, as he can percieve his own existence; he
>is certain of GOD, as a supreme being capable of the
>infinite, and thus an infinite being.
>
>According to Descartes we always have the freedom of saying
>"Yes" or "No" to any question or supposed act.

Here is another big assumption. He was drawn to it culturally, not philosophically.

>We can be
>free from making error, by making clear and distinct
>statements about our situation and the consequence.
>Descartes feel's that we carry a reflection of the infinite
>within our free will, and thus, a reflection of GOD. As,
>there are an infinite amount of questions or acts that we
>can say "Yes", or "No" to. Therefore, even though we cannot
>excecute the infinite, as a sign of respect from GOD to us
>human beings, we are capable of facing an infinite, and any
>amount of questions/acts with a simple yes or no,

Wait a second! Didn't you just say that our lifespan is finite? How are we gonna answer an infinite number of questions?

>thus,
>making use of our free will, which reflects the infinite,
>and thus GOD.
>
>Peace.

There is, unfortuantely, a thin line between philosophy and spirituality. If your description presents an accurate picture of the Cartesian argument (and of that I'm not sure, I'll give you the benefit of the doubt, but note as you did that you omitted details to save space), then I can only consider this argument an act of faith, and not of logic.