One sure way to win souls is to teach them the law. Sinners must know how they are committing serious evil against the Lord by disobeying God's law. Paul said he would not have known,"you shall not covet", if he had not observed the law. When you show a sinner that he has broken the law of God, then it can revive his dead soul, and bring him to salvation.
If you do not follow the law, or have a heart to follow the law, then this approach will not work, but this is the best approach. Show them that they are sinners, unable of receiving salvation apart from Jesus Christ.
I agree with brother James, in no way are those who are steeped and dead in sin going to want to be "saved" if they don't think they are perishing.
If someone told someone in the street that someone paid the ultimate price to redeem them of a death sentence and their million dollar fine was paid in full, they would not feel relieved. They would say, "What death sentence, I've not killed anyone, I haven't been prosecuted, I'm a good person and am innocent!" or "What law have I broken to get a fine?" But if they were arrested and hauled to court in chains and the judged sentenced them to a death sentence along with a million dollar fine imposed. Then someone came to them in their brokeness and said, "You have been REDEEMED from your death sentence and sent FREE and your million dollar fine has been PAID IN FULL, then and only then would they feel true JOY of knowing the love demonstrated by His Lord to them.
Act 13:39 and by him every one that believeth is justified from all things, from which ye could not be justified by the law of Moses.