I am "with you" that the fall indeed was a major game changer for mankind and our relationship with God. Do you see anything in the narrative of the fall and curse that indicates that mankind lost this ability?
Here are some reasons why a loss of this ability is indicated.
Immediately when Adam partook of the food, they were ashamed. When God sought them (though being God he knew where they were) the couple hid themselves. They didn't approach God. He sought them.
Remember pre-fall, Adam and God walked together each evening. It was the customary thing that they did. For Adam to hide from God, demonstrates no desire to seek God.
Secondly, the actual conversation between the characters.
Adam and the woman were face to face with God. Unlike any born of the flesh, there was a history of a daily friendly and intimate relationship from which they could all draw. But what is the reaction?
Shame, blame, excuse... Not once was there ever even a hint of reconciliation, apology, acknowledgement of sin in worship from humankind.
If ever there was a chance for repentance it was at that time. So, it is not only a question of ability, but of desire. And both are part of the fall. There is no ability and no desire of the natural man to seek or accept God.
Corrupted, warped, yes, but I personally still mankind still minimally"functional" in that man still seeks to worship "something" a constant stream in almost all cultures, tribes and peoples. We, I believe are lost, without God's grace, to our own devices, created god's and fruitless searches for meaning and purpose.
Because all human kind has been imprinted with the basic commandments of God which include the first four, there is also an awareness of a need to worship. However, look at the second to see the level of deceit and corruption that "all cultures, tribes, and peoples" use to exclude the one true God. This is also represented by Cain and Able.
Now as to you last thoughts, about decay etc. I realize I am in the vast minority around BB land on this, in that I think death and decay, are part of the natural created order and existed prior to the fall, this created order is by design naturally entropic. I do not believe that the fall brought this particular poison to creation. I see in the creation accounts hints that humanity was not created to live indefinitely in the first place, as indicated by the Tree of Life, and Adam's banning from it after the fall. I think the far more important message of death in the narrative of the fall is the chasm and separation from fellowship with God.
The basic problem with "death and decay" before the fall is that such is a violation of the nature of God.
Some point to the "tree of life" as showing there must have been death and decay in Eden, and that it is also found in the New Heaven as well.
However, careful study of the use of the phrase "tree of life" would show much clearer evidence of what this tree actually represents. For instance: Proverbs uses the phrase "tree of life" four times. Each time, it is a representation of a characteristic in which a believer may have. Certainly, one who possesses life of and in Christ lives with no decay and death, yet the tree is in the New Heaven? Look at the size and position of the tree?
Compare that to the statements that the Lord gave of himself.
Do not think that the tree of life was simply a tree that one would live forever. Just as the tree of the knowledge of good and evil brought far greater results than just knowing what was good and evil, the tree of life has much more emphasis than merely giving everlasting life which is found in Christ.
