Do all moral humans go to heaven?

Given a person X who leads a "moral life" based on the law laid out in the Bible. Given that X does not believe in the existence of God or any other God. If the Christian Faith happens to be the truth, can X be saved (meaning being accepted into heaven)? Can X be saved if X follows all laws, except for those who are calling for a direct relationship with God? Can X be saved if X follows his or her conscience, but because of lacking knowledge of the law is still sinning? What are the different positions on these questions of each denomination?