Is An "Age of Accountability" Found In The Bible?

I was having a conversation with someone (O.k., it was my father-in-law) and he suggested that babies who die are saved because they have not yet reached the age of accountability. He was unable to define what that age was and he seemed really flummoxed by my next question which was, "Are you suggesting that there is more than one way to be saved?"

My reason in asking that question is that I believe there is but one way, and one way only, to be saved, and that is to be born again. Paul describes it like this in Ephesians 2:8-9

For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
Not of works, lest any man should boast.

In other words, God gives the gift of faith. That faith enables us to believe. We don't work up faith, it is given to the elect.  In fact, it is given at a time when we are

dead in trespasses and sins

Ephesians 2:1

Dead people don't believe anything. They have to be made alive first. And it can happen to babies. Even babies in the womb.  If it can't happen to babies in the womb, then how can they be saved?  If babies can't be born again, and the Bible doesn't describe any other way of being saved, then babies can't be saved and they go to hell if they die. 

This is Mark Dewey's explanation of the subject.