I'm not done with my reading or work yet (it's about the importance of recognizing Christianity is no longer a western religion, but instead largely found in Latin America, Africa, & Asia, and what changes that causes in Christian academic work)... but I'll try & do a quick answer to the theodicy stuff.
In Genesis, during the 2nd creation story, an enemy is introduced with no background. Instead, it's just "the serpent was more crafty" (3:1). He eventually causes the downfall of the two humans, but not without a pronunciation of his impending doom (3:14-15... "he [the seed of Adam] will bruise your head, and you shall bruise his heel"). Later on, it is introduced that Satan was actually a fallen angel, who chose to love himself over God and thus rebel against Him.
(Edit: Satan is introduced in the same way, actually. He is suddenly just included into the story of Job as an accuser. That's it. No explanation as to how he got that position, or why he's there.)
Note that there is no explanation as to why the serpent (and then Satan) exists. It / he / whatever just is.
In John 9, there is a discussion between the apostles & Jesus (who is the seed of Adam mentioned in Genesis, according to Christianity - Judaism would disagree). They approach a blind man, and the apostles ask him the question based on wisdom of the day: "And his disciples asked him, “Rabbi, who sinned, this man or his parents, that he was born blind?” Jesus answered, “It was not that this man sinned, or his parents, but that the works of God might be displayed in him."
Note that Jesus does not answer why the man was blind. All He does is cure the blindness. The blindness just was.
Christianity does not seek to answer all the questions (one of the reasons why I got so mad at redwill's assumption that this was the reason for the religion, along with his really arrogant tone at the time). It simply seeks to introduce God. It does not explain why evil exists, but only that God & Jesus will fix it. Jesus, according to Christian history, is the apex of the curve. All things before Him (in terms of salvation) were working towards Him; all things after must now deal with the effects of that event. Again, Christianity does not try to explain why the frog exists, or how the planets orbit the sun, or what exists in the galaxy of Andromeda. It simply introduces God.
IMO, then, the question needs to be reduced if you want to look at theodicy in terms of Christianity. Do you trust this God? With all of the evil in the world - the Holocaust, the Khmer Rouge, the death of innocent babies, etc - do you still trust that this God of Christian Scripture exists & is capable? It is understandable to say no, and thus it is why theodicy is such a major deal. Christians would likely point to the events of the Bible (Jesus' death & resurrection, the power of the Holy Spirit in the new church, the salvation of Israel from Egypt, etc) as to why one should trust God despite this lack of understanding.
As an FYI, shmenguin, the idea of an unbaptized baby not being saved is an archaic Roman Catholic idea (I am not sure if they would still say that). Protestants would not worry about this, most likely.
People did not understand Jesus at the time of His (supposed) coming. The Jews demanded he be the messiah they expected, saving Israel from Rome. The apostles were part of this. The Jews did not understand God's actions when Jerusalem was destroyed & Israel (God's chosen nation) was defeated by a pagan nation - the book of Lamentations discusses this. The Apocryphal books discuss the struggles of Israel under their new kings (and thus question why God is allowing this treatment). Much of Christian Scriptural writing deals with God's people(s) not understanding what God is doing.
Christianity does not try to explain theodicy. It simply tries to introduce its answer - God & Jesus. Again, this is why I got so frustrated at redwill trying to turn religion into an "explain the gaps" BS, as if that's an obvious understanding. Obviously, a lot of theologians have attempted to tackle the theodicy question, but that's beyond my ability to discuss.
Now, going back to reducing the question. It is not the question of theodicy - it is the question of if you trust this god of Christianity. If you don't, then there's no answer sufficient for you for theodicy. If you do, then you'll believe despite the lack of answer, knowing that God somehow has a plan through all of this. Hence nobody's response, saying it doesn't bother him. Again, there has been many attempts by theologians to tackle it, but I'm not really convinced by any of them. I'm also not overly distraught by theodicy.
There has been discussion of love being impossible without free will. I'd imagine that's part of it. It's likely why Satan was allowed to fall - God was not going to force people to accept Him & love Him. That's not love; that's slavery. Does that account for the existence of AIDS? The reason for famine & death? I mean, original sin is an attempt to explain it, but that's not really satisfactory for people outside of the faith who don't really give a damn about it. There isn't really a satisfactory answer for all, even after years of studying it. But the faith does not disintegrate because it doesn't answer it; as I said, the point isn't to answer all the questions. I trust in God's ultimate plan, and I see bad things creating better situations all the time.
I say this as a person who's suffered through depression, divorce, suicide of friends & loved ones, death that comes too early for others (such as grandparents), and so on. I study Asian history, where massacres & such are much more common - 1 million people dying due to something is commonplace. It's a discussion I need to consistently think about.
It's not an adequate answer, and frankly, I don't care. It is an attempt to explain a worldview. I don't expect it to suffice redwill or shmenguin or anyone else. I expect it not to, to be honest. But, that's okay! As I've said many times, I'm not here to convert you guys. I'm just trying to answer a question & spread more understanding. This whole post is my own opinion - others will think differently.
Now, if you'll excuse me, I'm only halfway done with my work. Stop distracting me.