Can man correct what's wrong in his soul or spirit?
No. The soul and spirit are the invisible part of man's makeup, created by God, and nothing man can do can correct what is wrong there. Man cannot operate on or medicate the invisible. Only God can act in that realm, showing us we are sinners and moving us to believe the gospel.
Les explains that just as we can see and feel the effects of the physical, so it is with our spiritual makeup—the soul and spirit, the invisible part of us. They are the result of God's creative act. Since they are invisible, there is nothing man can do to correct something wrong in them. We cannot lay them on an operating table for surgery or give them a miracle drug. This is the area of man's makeup that only God can do anything with, He alone. So God promptly shows us we are sinners. When we understand that, the Holy Spirit moves us to believe the gospel, the power of God unto salvation. Les points to 1 Corinthians 15:1 as the gospel.