My friend :)
Don't forget to delve into Aquinas over and over. He puts all the "smart men" of the world to shame. Mr. Hawking is a great genius when it comes to particle physics, but what does that have to do with his authority to speak on philosophical matters? A man who can beat a thousand people at Chess and has every mathematical equation memorised, with total understanding in the mind, can still be wrong when it comes to logical thought processes. Who cares what Stephen Hawking things about God? If he believes God does not or cannot exist, he is simply not speaking the truth of the matter (whether he knows it or not).
St. Thomas said "The study of philosophy does not consist in the knowledge of what men think, but in the understanding of the truth". If Hawking is right, he's right... if he's wrong, he's wrong. Don't let human respect colour your opinions. Use your head. :) In the end, Christianity subsists in the logical knowledge that God cannot not exist.
Ponder and remember this:
God's nature is, itself, pure existence. He is the only substance that is truly real, the only essence that needs no other essence to create or sustain it. God's perfection rests in the fact not that God is glorious or majestic (adjectives), but in that He is Glory and Majesty (nouns), though being One Sentient Being. The most mind-boggling thing to contemplate is: God is all of His attributes, and all His attributes are totally simple, blended into one attribute, which is Himself. His essential nature is to exist, and His existence is His very essence; contrarily, we humans have an essential nature which is not to exist. We all come from - and are driving toward - non-existence, and that is essentially our natural state. God's natural state is to exist. His essence is to lack non-existence. Non-existence is not in God's purview or 'parameters' (were He to have any). He has no circumstances. He has no predicates. All existence is predicated on His existence.
Once the above notions are firmly established, it becomes easy to see that there cannot be another being that is omniscient and omnipotent. Please distinguish between "God cannot do it" and "it cannot be done". If God did not exist, this hypothetical omniscient, omnipotent being would be God. If God were to create it, however, God would not be God: because there would be another being extant that has divine attributes, which would then nullify God's own unique essence (which is to exist), meaning He isn't God anyway. This paradox isn't some clever wrap-around, but an easily refuted non-entity of an argument. It's not that God cannot do it; it's that the very nature of reality makes the idea stupid and impossible.
The answer to the question "can God create a boulder so heavy He could not lift it?" is, as always: "there's no such thing as a boulder so heavy God could not lift it; consequently, it cannot be created here, now, or ever, in any reality or by any power because it is a contradiction". In the same and likewise fashion, two omnipotent and omnipresent beings simply cannot exist; logically, causally, and metaphysically, it is an impossibility. This puts no constraints on God, but is a proposition at the very foundation of being itself. God does not contradict.