C.S. Lewis presents a fairly elegant argument for a "law of conscience" as evidence for a creator in Mere Christianity where he refers to it as a "sense of ought." It's a good read. There surely is a natural law, as Paul argues in Romans 2, but there are also moral precepts that become apparent only by revelation (scripture), no matter how sensible they seem afterward, to the mind informed by the Spirit. The Bible is not exhaustive in delineating sins, as you say, but sets forth both specifics and principles apart from which we will not understand what God expects of us.

Rom 7:7 What shall we say, then? Is the law sin? Certainly not! Indeed I would not have known what sin was except through the law. For I would not have known what coveting really was if the law had not said, "Do not covet."
(from New International Version)

Rom 8:5-8 For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit. 6 For to be carnally minded is death, but to be spiritually minded is life and peace. 7 Because the carnal mind is enmity against God; for it is not subject to the law of God, nor indeed can be. 8 So then, those who are in the flesh cannot please God.
NKJV

I believe that Romans 8, especially the verses cited above, and 1 Corinthains 2:9-16 are directly relevant to Hebrews 8:8-13. When Paul write this:

Rom 13:8-10 Owe no one anything except to love one another, for he who loves another has fulfilled the law. 9 For the commandments, "You shall not commit adultery," "You shall not murder," "You shall not steal," "You shall not bear false witness," "You shall not covet," and if there is any other commandment, are all summed up in this saying, namely, "You shall love your neighbor as yourself." 10 Love does no harm to a neighbor; therefore love is the fulfillment of the law.
NKJV

...it's along the same line as discussing the mind controlled by the Spirit, or having God's laws written in our hearts. To the extent that we have "the mind of Christ" we'll do what is right and not what is wrong because we do love others and are not self seeking. But we still need some information to guide us to that mind, and to inform our intellects of standards that truly are in the best interests of others and ourselves.