I agree that dismissing large swaths of the Bible makes the whole thing pointless. But what if the Bible, especially the Old Testament, was never the modern-style historical catalog of events that Evangelicals assume it is? The most recent pieces were written two millenia ago, and people had a very different idea of what a history was supposed to do. The Old Testament is even older, and as far as I can tell it is the collection of Israel's understanding of what happened to them, who they think God is, and what they think God wants of them. So the truth claims are about who man is and who God is, not "these are the events exactly as they happened". George Washington didn't cut down the cherry tree, but the point of the story is that he was truthful, which is historically attested to. So is the story wrong? Yes, the events never happened, but no, it is correct about Washington's character.

Gen 1-11 (Adam and Eve, the flood) should be read in the context of the mythology of the other nations. [1] Most creation myths had the gods create man to serve the gods, and they got too noisy, so they wiped them out with a flood, except one of the gods saved one family. In contrast, Yahweh creates people in his image, and it is our disobedience that leads to the flood. Whether or not there was a flood is not really the point--everyone at the time assumed there had to have been a flood, because you find fossils of sea creatures on the tops of mountains. (And perhaps more relevant is that God separated the waters of Chaos to make an orderly creation, and our sin almost resulted in the undoing of creation but for the faithfulness of Noah.)

Ultimately the only historical claim that Christianity really rests on is the resurrection. We know there was a guy named Yeshua from both Josephus and references in the Talmud, and they fit the general picture of the Gospels (keeping in mind that the authors of the Talmud were obviously not favorable to him). Beyond that we don't have much history. I've always found C.S. Lewis' argument persuasive: a first-century Jew would not think to claim that they are God yet Jesus did, and his twelve followers maintain that assertion in the face of death. Nobody could produce a body, even though it would be in the disciples' self-interest to. Either Paul or Luke claims there are 400 people that saw Jesus after the resurrection, with the strong implication of "go talk to them if you don't believe me".

I've also found the argument of a psychologist I met persuasive as I've gotten older: each of us has some minimum standard of behavior which we require of ourselves yet fail to meet, and at some level we are not okay with it and feel guilty. That's rather odd. C.S Lewis' argument about beauty (beauty serves no utilitarian purpose; there's no reason the world need to be beautiful--indeed, American suburbs are not--yet it is beautiful. That's odd.) I think the one of the strongest arguments is that the Bible's description of human nature is pretty accurate.

But generally all we get is a bunch of places where having no God creates problems with the model, and if God does exist, it resolves the problem. Of course, the reverse is true, and so you find the Bible dealing with those (why evil in Job, Psalms, Jeremiah, Habakkuk, for instance). I'm still in the process of resolving these questions myself, but I think the question in this stage is "do I want to follow God/Jesus if he does exist with the character described in the Bible?" God might not exist, in which case I will be heartbroken, not only because I want that God, but also because the only other option is meaningless. The atheism of the twentieth century offers a grim warning of this path: you can see it in art, where a toilet was a poignant piece; you can see it in the destruction wrought by atheistic Communism which destroys beauty and killed more people than WWII; you can see it in our own society right now, with elites finding meaning in activism, which has to be ever more extreme in order to still have something to change. If Christ was resurrected there is beauty, there is redemption of man to God and man to man, there is purpose in life. Some days I'm not sure if the evidence favors God, but fortunately Christianity is based on more than just historical claims from projecting a modern expectation onto an ancient text.

[1] I recommend Understanding Genesis by Nahum Sarna (written from a Jewish perspective). There's a summary at http://geoffprewett.com/BookReviews/UnderstandingGenesis.htm...