Here are St. Thomas' Five Ways for you that prove the existence of God. I'll next post Thomas' thought on the Trinity and Reason.
THE FIRST AND MORE MANIFEST WAY is the argument from motion. It is certain, and evident to our sense, that in the world some things are in motion. Now whatever is moved is moved by another, for nothing can be moved except it is in potentiality to that towards which it is moved; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be moved from a state of potentiality to actuality, except by something in a state of actuality... it is therefore impossible that in the same respect and in the same way a thing should be both mover and moved i.e. that it should move itself. Therefore, whatever is moved must be moved by another. If that by which it is moved must itself be moved, then this also needs to be moved by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and consequently, no other mover, seeing as subsequent movers move only inasmuch as they are moved by the first mover; as the staff moves only because it is moved by the hand. Therefore it is necessary to arrive at the first mover, moved by no other; and this everyone understands to be God.
THE SECOND WAY is from the nature of efficient cause. In the world of sensible things we find there is an order of efficient causes. There is no case known (neither is it, indeed possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, whether the intermediate cause be several, or one only. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, or intermediate, cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God.
THE THIRD WAY is taken from possibility and necessity, and runs thus. We find in nature things that are possible to be and not to be, since they are found to be generated, and to be corrupted, and consequently, it is possible for them to be and not to be. But it is impossible for these always to exist, for that which can not-be at some time is not. Therefore, if everything can not-be, then at one time there was nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist begins to exist only through something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence - which is absurd. Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has already been proved in regard to efficient causes. Therefore, we cannot but admit the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God.
THE FOURTH WAY is taken from the gradation to be found in things. Among beings there are some more and some less good, true, noble, and the like. But more and less are predicated of different things according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest, and, consequently, something which is most being, for those things that are greatest in truth are greatest in being... Now the maximum in any genus is the cause of all in that genus, as fire, which is the maximum of heat, is the cause of all hot things, as is said in the same book. Therefore, there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God.
THE FIFTH WAY is taken from the governance of the world. We see that things which lack knowledge, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that they achieve their end, not fortuitously, but designedly. Now whatever lacks knowledge cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is directed by the archer. Therefore, some intelligent being exists by whom all natural things are directed to their end; and this being we call God.
***Here are St. Thomas' Five Ways for you that prove the existence of God.***
Allow me to post from one of your own Roman Catholic theologians and apologists...
"Not all the arguments (Twenty Arguments For The Existence Of God - includion Aquinas' 5 Ways) are equally demonstrative. One (Pascal's Wager) is not an argument for God at all, but an argument for faith in God as a "wager." Another (the ontological argument) we regard as fundamentally flawed; yet we include it because it is very famous and influential, and may yet be saved by new formulations of it. Others (the argument from miracles, the argument from religious experience and the common consent argument) claim only strong probability, not demonstrative certainty. We have included them because they form a strong part of a cumulative case. We believe that only some of these arguments, taken individually and separately, demonstrate the existence of a being that has some of the properties only God can have (no argument proves all the divine attributes); but all twenty taken together, like twined rope, make a very strong case."
- Peter Kreeft
http://www.peterkreeft.com/topics-more/20_arguments-gods-existence.htm
And that's just my point. These arguments, as convincing as they are, can in the end only make a "very strong case" and not a "proved by reason in a flawless argument."
P.S. I've used many of these arguments in conversation with others - I do appreciate their value.