This is a good question and one that I am going to prayerfully try to answer well. Two issues you bring up I want to deal with here:
I want to clarify that the belief or faith that is exercised by the believer is not blind, dumb, etc., however it is a faith that is reasonable. A faith that is informed. Winfried Corduan in "No Doubt About it: The Case For Christianity" states that even though we can only be redeemed through "saving faith," [saving faith is the faith that saves us: please see Acts 16:31; Galatians 2:16; Ephesians 2:8-9; Acts 4:12] such "saving faith" does presuppose some essential items of knowledge. He goes on to rightly point out that James states that the devils believe that God is one, but tremble, for they cannot be saved by such knowledge (Jas. 2:19). Neither are we "saved" by knowledge [alone], but the genuine "saving faith" that a believer exercises presupposes some knowledge along with that faith.
Note: To share a part of my personal testimony with you, I was an agnostic when I accepted Christ... A seeker who was very skeptical, I couldn't deny the truth of the scriptures as they were presented to me.
Jesus did not die on the cross to help us with any problem except our sin problem (Matthew 1:21). As a result of our salvation our quality of life improves, however. We have the hope of heaven, we have the peace that our sins are forgiven, and we have the assurance and comfort that comes along with knowing the word of God. Jesus said (another example of His teachings pointing to Him) I am the way the truth and the life no man comes to the Father but by me. This is why we rely on Jesus... The scriptures explicitly teach that it is through Him that we gain eternal life.
