I apologize for the length of this answer, but I have shortened it as much as I can without losing some very important facts.
All Scripture is quoted from the King James translation.
Having read your question and the comments and the answers several times I felt compelled to add my understanding of the Scriptures concerning this question.
Your question takes into account both the old and new Testaments. However, I think you may have missed one central point which is highlighted in the difference between the Old Testament and the New Testament. The Old Testament is essentially and introduction to the New Testament. By that what I mean is that without the Old Testament to look at; We could not understand Jesus mission and why things had to be the way they are. Let us take a look at the Old Testament, and how it relates to the New Testament.
What did I mean by saying that the Old Testament was an introduction to the New Testament? Essentially the Old Testament explains the need for a Messiah, Christ, the Savior. You are correct in your assumption that the law was given to the Jewish nation, and the reason for that was that this was God's chosen nation; and by that is meant that this was the nation through which God had decided to facilitate the salvation of man. So why did man need salvation to begin with?
When God created man; God created man with a free will, but free will has no meaning unless there is a choice. God gave man that choice by placing the tree of the knowledge of good and evil in the garden of Eden. What we need to take into account about this is that it is not the knowledge of good and evil, which makes man unacceptable to God. God himself has the knowledge of good and evil as did Jesus when he was on the Earth. Also we must understand is that God created both good and evil. This is obvious from the fact that there was rebellion in heaven; which of course is evil , and at the same time there were good Angels defending the Lord; and this prior to God's creation of man.
As with taking a single verse from the Bible and trying to understand its meaning without taking into account the remainder of the chapter, and the book, it does not lead to complete understanding.
Here is an example:
John 17:11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
Taking this verse alone, we are left with no true understanding of what Jesus is saying. However, in light of these other versus we get a better understanding.
John 10:26 through 30 But ye believe not, because ye are not of my sheep, as I said unto you. My sheep hear my voice, and I know them, and they follow me: And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand. My Father, which gave them me, is greater than all; and no man is able to pluck them out of my Father's hand. I and my Father are one.
When we take into account these other versus we understand that what Jesus was saying is that he and his father have predestined certain people to be saved. And when we expand our text to include the entire chapter, we understand that Jesus is here talking to the to the Pharisees. I will not quote the entire chapter here for the sake of brevity, but you can read the remainder of the chapter for yourself. And expanding our reading further to include the entire book of John we come to understand that what John is doing is explaining not only why people need salvation but the method by which they can obtain it. In order to fully understand we must take this same process to the entire Bible.
I stated that the Old Testament was an introduction to the New Testament. So exactly what did I mean by that statement? The Old Testament, beginning with Genesis 1:1 through Malachi 4:6 we find it is a history showing alternately the disobedience of God, God's reprisal, and finally, man's re-acceptance of God's will.
The significance of that cycle lies in the fact that even though man rejects God that God is forgiving and will accept man upon man's repentance.
Therefore the message of the Old Testament is summed up in:
Romans 3:23 For all have sinned, and come short of the glory of God;
So what does all of this have to do with your original question?
This is actually the message of the gospel, and what we have to understand is that a benevolent God created man out of love and as with all of his other creations God not only desired that these creations be made but that they be eternal.
Genesis 1:31 And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.
At this point we have to remember, that the world and man were all pristine when God pronounced everything as very good. But it did not remain that way due to the disobedience of man, and in doing so man knew what the punishment for that disobedience would be; and in rebelling, accepted God's promise of retribution.
Genesis 2:16 and 17 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat: But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
In the verses above we learn two things;
God provided all of man's needs in that he gave him every tree of the Garden except one.
We learn a basic fact of the nature of man in that he was not satisfied with God's abundance, but desired to have it all even to the point of suffering God's ire.
After having giving you the background. Now we shall take a look at the selection of the nation of Israel as God's chosen people.
To begin with, We need to analyze God's association with Abraham and the Abrahamic covenant.
Genesis 15:6 And he believed in the LORD; and he counted it to him for righteousness.
The key here is the that belief in the Lord is counted as righteousness, and that then is the key to salvation, that being that we believe and trust God. By that I do not mean that we believe that there is a God, but that we believe that he not only has our best interest at heart and that he loves us beyond our knowledge, but that we trust that he will provide all of our needs and the thing which separates us from God is our greed and desire for everything, and not just what God knows is our needs.
Matthew 6:8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.
Matthew 6:32 (For after all these things do the Gentiles seek:) for your heavenly Father knoweth that ye have need of all these things.
Here I'm skipping over some important stuff because this is basically far too long. However, I will be happy to give the rest of this to you in chat if you will bear with the fact that I am very very slow in the chat.
So to the point of Jesus, saying that he came not to do away with the law, but to fulfill the law.
What Jesus meant by this was that if you look back at the nation of Israel. They have not stayed true to the word as they should have, and by not doing so they have forfeited God's protection. However, if we take a look at John 3:16 and 17.
John 3:16 and 17 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
If we substitute the words 'his creation' for the word the 'world' we gain a better understanding of God's motives. Then at this point we go back to what God said to Abram in that God credited Abram with righteousness because of his belief.
'Abraham believed God, and God credited it to him as righteousness.' That same precept applies to us in that our belief is credited to us as righteousness. If we applied that to the gospel. What we find is that salvation does not actually depend upon Jesus death and resurrection, but upon our belief that his death and resurrection, paid our sin debt in full. You may think that is a foolish statement, but let's take a long look at it.
Luke 1:26 And in the sixth month the angel Gabriel was sent from God unto a city of Galilee, named Nazareth,
Matthew 1:21 And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.
In Luke, chapter 1 verse 26, We find that Gabriel is sent from God. And In Matthew, chapter 1 verse 21, we learned that God is telling us that Jesus will save us from our sin. But when we contrast that with John 3:16, we find that. John says those who believe will be saved. So how do we resolve the apparent disagreement between the two?
In order to blend these two. We have to go back to God's ascribing righteousness to Abraham for his belief. If we were to take Matthew, chapter 1 verse 21 in a literal sense we would have to accept this that Jesus death and resurrection would have covered the sins of everyone. This however is not true. Jesus himself said, that his sheep would hear his voice, while those that were not his sheep would be listening for their masters voice.
This can only mean that not everyone was saved by Jesus death and resurrection, and so we are left only to believe that what John said is true that only those who believe, are saved.
So how does this answer your question the answer is, quite simply, that the law has not been done away with; but instead it means that the law is still just as much in effect today as it was when God gave it. the difference is that through our belief our sins are washed away by the blood of Jesus. So therefore I can only determine that those who do not believe Jesus was the Messiah remain under the law. And those who have accepted salvation, even though they are still under the law, their disobedience of the law has been forgiven because they believe that Jesus sacrifice has obliterated their disobedience