Rom.2:15 "They [Gentiles] show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them."
This is the sort of text (perhaps the text-of-texts) that gives evidence that man by nature, according to his elemental constitution (spiritually) remains in possession of the moral law, albeit in a deformed fashion. The "work" of the law remains in his heart, and the evidence of it is the fact of personal conscience.
Paul argues that all men are culpable, even those who do not have special revelation to tell (remind) them what God's will for them is. A conscience may be misinformed and the moral compass stopped. But it is still correct once in a while (so to speak), like the stopped clock. When a man violates his personal standards (and everyone does), and that law happens to coincide with the law of God, God will convict him of his just deserts (hell) on the basis of that crime alone.
The work of regeneration, the Spirit and the Word, is a work of renovation. The tablets of commandment may have been smashed (as when Moses illustrated the Israelites broken covenant), but they were rewritten, Ex.34:1. The heart is a tablet of sorts, to be written upon, Prv.3:3; 7:3; Jer.17:1; 2Cor.3:3, "And you show that you are a letter from Christ delivered by us, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts."
Jer.31:33, "For this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people." This is the work of renewal.