Determinism.....

[Ryft]

Compatibilism just seems like determinism with free will defined slightly differently to make it sound nice.

Free will is not being defined differently so much as properly, foremost by the rejection of "free will" as a misnomer because the will is not free. I once shared your confusion because, perhaps like you, I persisted in the notion that the will is free, but it was a confusion that disappeared when I let go of that idea, substituting it with "free agency" instead. But I had to be shown the incoherence of "free will"—how it creates a dissonance in our intuitions and is violently inconsistent with a biblical world view—before I was able to drop it and pursue a more coherent view. Indeterminism or "free will" simply does not work. But neither does determinism, which, when held consistently, results in the nihilistic repudiation of truth, knowledge, science, etc. Evidently the truth was somewhere in between. Ergo, compatibilism. It is coherent and consistent biblically, logically, intuitively, and scientifically.

In the second-to-last sentence you say that determinism is real. So do you believe our lives couldn't ever have gone any differently, that our choices are in fact a combination of genetics and events happening to us?

What I choose is determined by my will. What I will is determined by my character and desires. What my character and desires are is determined by my experiences and genetic makeup. What my experiences and genetic makeup are is determined by God. That is undeniably a causal series, so in one sense determinism is real. But as I had said, that causal chain runs through the agent's conative faculties, not irrespective of them but concordantly with them. And yet our conative and volitional faculties do not passively respond to this causal chain but in fact actively shape it. To put it another way: What we do is not irrespective of any reason, as indeterminism says, but for a reason; and that reason is not irrespective of us, as determinism says, but shaped by us.

How can we be morally responsible if we are a mere product of our birth and environment?

Because we are not automaton passively responding to the causal chain, but free agents actively shaping it.

If two people are given the same opportunity to do good, why would one choose good and the other choose evil if "nature and nurture" only gives a tendency towards good or evil? How can we make a free choice between the two? We can't have a natural virtue to do good since that is deterministic, and it can't be random since random isn't free.

Because there is more at operation than just "nature and nurture," which never inclines a man toward good at any rate but only evil (wherein the terms 'good' and 'evil' are being used consistent with the Christian view, not an anthropocentric view). That is, we do not have "a natural virtue to do good." The expression Augustine gave us for this condition was non posse non peccare (unable to not sin). Although everyone is naturally born and a slave to sin, some are later spiritually born and a slave to Christ. Only those spiritually born in Christ then have a tendency toward good or evil (posse peccare, posse non peccare) because of the additional operation of the Holy Spirit at work in their lives. Regeneration (Gk. gennao anothen, born of above) is the difference between those who choose to do evil and those who choose to do good (e.g., Phil. 2:13). Man's will is free in the sense that his choices are a product of his own faculties, his own intellect and desires, influenced by his own character and heart. But it is for those precise same reasons that man's will is not free, because man's character, intellect, desires, etc., altogether are corrupted under the bondage of sin. Consequently, the degree to which man's will is free is proportionate to the degree that man is free from his sinful nature. And for the unregenerate sinner, he is not free from his sinful nature at all.