Brother, the distinction between spirit and soul is real, but the conclusions you’re drawing from that distinction are not found anywhere in Scripture: the Bible never says the human spirit is an incorruptible “deposit from God,” never says it remains untouched by the fall, and never says it merely becomes “disconnected” rather than dead; instead, Paul says the inner man is what must be made alive (Eph 2:1), renewed (2 Cor 4:16), and recreated (Eph 4:24), which only makes sense if the human spirit itself is fallen. When you say “man’s spirit has no bearing on the life of the man unless connected to God,” you’re actually agreeing with Paul’s point: the natural man cannot receive the things of the Spirit (1 Cor 2:14) because his spirit is not neutral — it is incapable until God gives a new one (Ezek 36:26). And your claim that the unrighteous man’s spirit “returns to God” while his soul is destroyed in hell is not taught in Scripture; Ecclesiastes 12:7 refers to the breath of life, not the human spirit being absorbed back into God. Likewise, “born of the Spirit” in John 3 is not the human spirit reconnecting with God — Jesus says it is a birth from above, a new creation, not a reactivation of an old spark.
As for conviction, the Spirit convicts the world because His work is external proclamation, not internal cooperation; He exposes guilt, but only those whom the Father draws respond (John 6:44). Conviction is universal; regeneration is not. The fallen spirit does not assist conviction — the Spirit of God does. The issue is not universal salvation; the issue is that Scripture presents the human spirit as fallen, dead, and in need of new creation, not as a dormant divine deposit waiting to reconnect.
I don't think we disagree on the main parts, only on it's application.
The natural man includes his body, mind and his soul. These are opposed to God. While unredeemed, his spirit is dead: unable to affect his life.
You almost got it: referencing the breath of life. God is spirit and so He gives spiritual things. Why not simply let the breath disperse after a man's physical death? Why not let it become part of the atmosphere? Because its origin is God who gave it. That breath ultimately belongs to Him and so it returns to God upon a man's death. "Is it a physical thing?" No. God is Spirit.
And, regarding conviction by the Holy Spirit: which part of fallen man "receives" the conviction? Remember, it is the work of the Holy Spirit. If man "cannot receive things of the Spirit" (1 Cor 2:14) then how can fallen man become convicted? Furthermore, how can fallen man resist God if he cannot receive the things of the Spirit? Why oppose God's Spirit at all? Why not simply ignore God? But man cannot ignore God. Indeed, even creation testifies of His invisible characteristics. Unbelief is active and intentional.