It is a sad reflection on our cold-heartedness that we can sin without being bothered about it. Or even that we watch the sin of others and not be touched. Simple rules of just reading the Bible and getting in touch with the emotions are not the answer. They lead to legalism. The only answer to sin is in God himself.
Sin is a breakdown of relationship.
The Old Testament is not just about law. It has grace as well. The psalmist knew this and he could turn to God for grace according to His law, for the psalmist knew the scripture. There is nothing in the New Testament that equals the Old Testament in describing the grace and compassion of God. God does not repay us with what we deserve.