Do you then hold that man retains, even after the fall, the ability to exercise faith and turn to God apart from grace?
All I have stated, Bob, is that God is pleased with self-sacrificing acts of love. He is pleased with such acts, no matter who performs them.
Most non-Christians as well as non-Christians, though they may be kind and gentle, will not sacrifice themselves for the sake of others. But a few will, even among those who have never tasted of the heavenly gift.
All people exercise faith. We cannot live a moment of our life without doing so. When you are about to sit in a chair, you exercise faith that the chair will support you, probably basing your faith on past experience with chairs. When you enter your car and turn on the key, your action show that you believe the car will start.
The faith we exercise in God is not of a different order from the above. It differs only in the object of our faith.
And Jesus, responding, says to them, "Have faith in God." Mark 11:22
Jesus seemed to think that his disciples simply through the exercise of their wills could have faith in God. They did not yet receive the abiding presence of the Holy Spirit which they later received on that special day of Pentecost.
Because of free will which God has given man, a person is also capable of turning to God whenever the Father draws him, that is, creates circumstances which invite him to do so. Perhaps the Father sends one of his servants to him with a word. Perhaps the Father uses some circumstance in the person's life to influence him.
I think the Calvinistic thinking about the grace of God is in error. Titus chapter 2 show what grace really is:
For the grace of God has appeared for the salvation of all people, training us to renounce impiety and worldly passions, and to live sensible, righteous, and pious lives in the present age, expecting the blessed hope, the appearing of the glory of the great God and of ourSavior Jesus Christ, who gave himself for us to redeem us from all lawlessness and to purify for himself a people of his own who are zealous for good works. Declare these things; encourage and reprove with total command. Let no one disregard you. Titus 2:11-15
Grace is God's enablement to work righteousness and to overcome sin. But he will not so enable us if we do not coöperate with his grace. It is the free exercise of our faith in God and his grace that provides the basis of our coöperation. Call it synergism if you will. But that's the way God works. We cannot consistently work righteousness through self-effort. Nor will God sovereignly work righteousness through us. But rather:
Working together with him, then, we entreat you not to accept the grace of God in vain. 2 Corinthians 6:1