There are three scriptures that define sin:
Romans 14:23 "…whatever is not from faith is sin."
James 4:17 " Therefore, to one who knows the right thing to do, and does not do it, to him it is sin.”
1 John 5:17 "All unrighteousness is sin…”
So we can see from these scriptures that the definition of sin is anything outside of God's will.
The question then is, are we born in sin? Yes. We inherited sin from Adam. 1 Corinthians 15:22, “For as in Adam all die, so also in Christ all shall be made alive.” So, it is clear that we are born sinful, and since everyone has inherited sin from Adam, plus Satan is the "god of this world" (2 Corinthians 4:4) we are also born into a sinful world.
But, we thank God that there is a way out, which will be for all mankind, as “in Christ ALL shall be made alive!”