Man's faculties didn't cease as a result of sin, they became corrupted. Man can still think and emote, but he does so differently than before sin. Man is able to live in the natural world. It is in the spiritual realm that he cannot operate well.
So then the ability to believe the Cross is plausible because understanding right from wrong and judgement between the two is all that is needed to believe the Gospel. If one can understand we are wrong, Christ is right and right leads to life and wrong leads to death they can respond to the Gospel of their own volition because God supplies the grace needed to keep the flesh in check so the will is free to respond. Not everyone prefers the dark Cameron despite what you might think of mankind.
1Cor.15:3-4
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, 4 that he was buried, that he was raised on the third day according to the Scriptures,
The new birth is needed for faith.