score:4
It can't have been his body, because he was still alive physically and didn't drop dead on the spot.
And it can't have been his soul because he felt naked after eating of the forbidden fruit. Which means his natural mind was still working.
And they heard the voice of the LORD God walking in the garden in the cool of the day: and Adam and his wife hid themselves from the presence of the LORD God among the trees of the garden. - Gen 3:8
The only part left of us is our spirit which we cannot perceive through our 5 senses.
That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. - John 3:6
So I believe it was a spiritual death, not a natural death.
Why was he driven out of the garden? I believe it was so that he couldn't continue to eat of the tree of life and continue to live physically forever in a fallen state.
And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: Gen 3:22
I believe it wasn't so much that sin had separated God from man, but man from God. It was man who hid from God in the garden after eating the fruit and man who felt shame. God continued to reach out to man but sin kept man away from God.
But obviously things were not quite the same. Without a spirit that is alive they were unable to fellowship with God. They (and we) cannot relate to God spirit to spirit unless we are born again.
Gen 3:8-10:
8 And they heard the voice of the Lord God walking in the garden in the cool of the day: and Adam and his wife hid themselves from the presence of the Lord God amongst the trees of the garden.
9 And the Lord God called unto Adam, and said unto him, Where art thou?
10 And he said, I heard thy voice in the garden, and I was afraid, because I was naked; and I hid myself.