You seem to want to bring this back to sin as if you have a strong sin consciousness. The question is: "How much of your sin did Jesus take upon Himself when He died on the cross?" And, how much of your sinful flesh did the righteousness of Christ cover? The answer to those questions will show how much of a Saviour you think Jesus is.
I want you to now think of a pink elephant in striped pajamas. Form that image in your mind. Now, I want you not to think about the pink elephant in striped pajamas. While trying not to think of the elephant, close your eyes. What do you see?
This is what being preoccupied with sin is all about. Sin is the pink elephant in striped pajamas. It dominates your thinking. As much as you try to stop thinking about sin, it still occupies your mind, and therefore your preoccupation with sin colours your Christian experience. So when you pray, read the Bible, or do any other duty to God, the thought of sin comes in and interrupts. It is like trying to read the Bible when a group of rowdy hooligans are whooping it up right outside your window. The intrusion is not welcome, because you want to pray and read your Bible, but the intrusion is distracting you.
That is what preoccupation with sin is like. Satan is the interrupter. When you want to pray, read your Bible, or serve God in any other way, he reminds you of how sinful you are. He harasses you with your faults and failings so that you can't concentrate on pray and Bible study.
You have to lay your sin and sinfulness on Christ, and allow His righteousness to totally cover it. Start thinking about His righteousness, His love, His grace and mercy, His blessings on your life, and allow those to dominate your thinking.