Your claim that the Bible does not distinguish between a general call and an effectual call completely ignores the explicit vocabulary of the New Testament. No one disputes that the outward preaching of the gospel goes out generally to everyone who hears it. But the Apostle Paul explicitly outlines a specific, sovereign call that is distinct from the mere sound of a preacher's voice.
In Romans 8:30, Paul outlines the unbreakable golden chain of salvation writing that whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.
Look at the absolute mathematical certainty of the text. 100 percent of the people who receive this specific call end up justified and glorified. If this call simply meant the outward preaching of the gospel, then everyone who has ever heard a sermon would be justified and go to heaven. Since we know that is not true, the Bible explicitly teaches an internal, effectual call of the Holy Spirit that successfully secures the salvation of the elect.
Furthermore, your idea that Adam's spirit died but his soul remained untouched and fully functional is a completely fabricated invention. The Bible never teaches that human beings are divided into separate compartments where the spirit can be dead while the soul remains morally pure and spiritually healthy.
In Romans 3:10-11, Paul quotes the Old Testament to define the total, absolute corruption of the entire unregenerate human being stating that there is none righteous, no, not one: there is none that understandeth, there is none that seeketh after God.
If the human soul was still spiritually alive, alert, and healthy enough to seek after God on its own, Paul would be wrong. But the text says there is none that understandeth and none that seeketh. The corruption of the fall affected the entire man—his mind is darkened as per Ephesians 4:18, his heart is deceitful and desperately wicked as per Jeremiah 17:9, and his will is in absolute bondage to sin as per John 8:34.
When you hear a sermon, your physical ears can process the sound and your natural mind can understand the words. But a dead, unregenerate heart is fundamentally incapable of loving the truth or submitting to it. As Romans 8:7 explicitly states, the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
An enemy with a hostile carnal mind cannot choose to obey the gospel until God performs the exact heart surgery promised in Ezekiel 36:26, removing the stony heart and giving a heart of flesh. You do not respond to the call to get made alive; the sovereign voice of Christ effectively makes you alive through the new birth, causing you to willingly, joyfully respond. The text has spoken, and salvation belongs entirely to the Lord from start to finish.