Descartes' ontological argument is distinctive in that it makes use of a concept of causality that is not present in Anselm's version. Roughly-stated, Descartes argues:
1. I have the mental concept of a perfect being. (Premise)
2. The mental concept of a perfect being is either caused by a perfect being or an imperfect being. (Premise)
3. The mental concept of a perfect being cannot be caused by an imperfect being. (Premise)
4. Hence, the mental concept of a perfect being is caused by a perfect being. (From 1-3)
5. Therefore, a perfect being exists. (Conclusion)
This argument is one of several proofs of God's existence found in Descartes' treatise, Meditations on First Philosophy. I take it that Descartes, like Anselm, conceives of a perfect being as an entity that possesses omnipotence, omniscience, moral perfection, and necessary existence.
Unlike contemporary modal treatments of the ontological argument (usually a refurbishing of Anselm's proof), Descartes' argument does not make use of S5 or the Barcan Formula. Nevertheless, one who challenges the possibility premise of (1) won't accept the argument anyway. On the other hand, one who accepts (1), but rejects S5 for whatever reason, may find Descartes' argument more appealing. There are, in fact, some notable modern defenders of the argument. 
(2) assumes that there really is a causal relation between the mind and the mind's concept of a perfect being. This is generally granted, unless one adopts a radical Humean position with respect to causality.
Since (4) and (5) are deduced from the first three premises, the most likely premise to be rejected by skeptics is (3). It is at this point that Descartes is tapping into the intuition that imperfect beings, such as ourselves, are incapable of actualizing any perfection whatsoever, at least by ourselves. Since I lack the power to do certain things, I cannot make myself omnipotent, for instance. This aspect of (3) is probably uncontroversial, but what about mere concepts? Should our imperfections lead us to believe that we cannot be the source of our ability to conceptualize a perfect being?
I will simply let the reader decide for him/herself.
 See, for example: Clement Dore, Theism, Springer, 1984.