In the fall, all of Adam's faculties such as love and faith became tainted by sin. This also was passed down to all his posterity. The unregenerate have faith in everything BUT God. This faith is innate and will save nary a soul. The unregenerate have love in everyone/everything BUT God. This love is innate and will save nary a soul.
In the divine quickening, the unregenerate is regenerated and infused with love and faith and they exercise them in salvation. That is why it is said "thy faith has saved thee".
And that is why the discussion came down to Cain.
It is obvious that Cain did have faith. When he offered his sacrifice we determined that he did not offer his sacrifice in faith but rather in rebellion to God. He was jealous of his brother Abel, as the account describes.
But it was his choice. He had a free will. He chose to rebel.
Cain could have submitted to God's will and could have offered a blood sacrifice as God commanded him to do. There was nothing preventing him to do so. God was not forcing him to offer a sacrifice of his own works. He chose to go that way. It was not a result of his fallen nature, for Abel had that same nature.
Even after Cain offered that sacrifice of works and had rebelled, God spoke to him, and urged him to do the right thing.
Genesis 4:5 But unto Cain and to his offering he had not respect. And Cain was very wroth, and his countenance fell.
6 And the LORD said unto Cain, Why art thou wroth? and why is thy countenance fallen?
7 If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door. And unto thee shall be his desire, and thou shalt rule over him.
Cain still had the opportunity "to do well," to offer a blood sacrifice. The Lord pleaded with him, though he was "unregenerate," as you would conclude.
So we conclude:
Sin separated Cain from God.
It appears that through his rebellion he was unregenerated.
Though he was unregenerated, God was still able to speak to him and he did. Thus Cain's separation from God (his spiritual death) did not prohibit God speaking to him.
His offering to God was his free choice. Both before God rejected it and after God rejected it, God gave him the opportunity to freely sacrifice of his own will. But he chose to rebel. He wasn't forced to.
The same is true today. The very last invitation in the Bible is:
Revelation 22:17 And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely.
This invitation is without condition. It is typical of every invitation that the Lord has ever given. Come and take of his gift of salvation freely. Whosoever will may come and take freely.
There are no conditions. The depravity of man does not interfere. Any man is able to come.
That teaching is so clear in this verse. Anyone can come to Jesus. There is no one that he will cast out.
Tell me, is there any one that Christ ever refused?