I have spent quite a bit of time defending the Modal Third Way. However, I think the traditional argument is compelling, as well. What Maimonides, Thomas, and others have argued is the following:
1. Every existing entity is either contingent or necessary. (Definition)
2. Something has always existed. (Premise)
3. There was a past time at which nothing contingent existed. (Premise)
4. Therefore, a necessary entity exists. (From 1 - 3)
Before moving on to a defense of each of the premises, a few words of "necessity" are in order. First, the conclusion is not necessarily to a logically necessary entity. It's not as if "nothing necessary exists" is contradictory in the same vein as "John is a married bachelor." Rather, the argument seeks to establish the existence of some temporally necessary entity, e.g. something indestructible, or incorruptible, if it exists at all. Moreover, as I have said on more than one occasion, a necessary entity must also be eternal and enormously powerful (if not omnipotent). After all, the weaker a thing is, the more inclined it is toward corruptibility.
Now, what about the argument's premises? (1) is obviously true: an existing thing either possibly fails to exist (contingency) or cannot fail to exist (necessity). (2) is based on ex nihilo nihil fit (out of nothing comes nothing). If there were a past time at which nothing exists, then nothing would exist now, which is patently false.
(3) is likely the most controversial premise, but "controversial" is not synonymous with "improbable." Given infinite time, all non-zero probabilities will be actualized at some point. The Scholastics put it like this: given infinite time, all real potentialities will be actualized. After all, infinity is just inexhaustible. In fact, it could even be argued that there are infinitely-many points at which nothing contingent exists. Either way, (3) appears to be in good shape. Yet, if nothing contingent existed at a past time, and something existed at the same time - per premise (2) - it follows that a necessary entity exists.
Therefore, something necessary, eternal, and enormously powerful exists. Whether or not this entity is the Christian God, or the deity of any other religion, is a matter for further inquiry.
Of course, one could always say that the universe's past is finite, and I would agree. However, that does nothing to undermine the Third Way. In fact, it actually gives us another argument for God's existence: the Kalam Cosmological Argument (KCA).