Hi,

Obviously there are quite a few reasons why God gave the law. The Heaven test focuses on what the New Testament says concerning this in regards to salvation. Here are some of the key verses concerning this:

Rom 3:19 " Now we know that whatever the law says, it says to those who are under the law, so that every mouth may be silenced and the whole world held accountable to God. ²⁰ Therefore no one will be declared righteous in his sight by observing the law; rather, through the law we become conscious of sin."

Rom 5:20 "The law was added so that the trespass might increase. But where sin increased, grace increased all the more,"

Gal 3:19-25 "What, then, was the purpose of the law? It was added because of transgressions until the Seed to whom the promise referred had come. The law was put into effect through angels by a mediator. ²⁰ A mediator, however, does not represent just one party; but God is one.

²¹ Is the law, therefore, opposed to the promises of God? Absolutely not! For if a law had been given that could impart life, then righteousness would certainly have come by the law. ²² But the Scripture declares that the whole world is a prisoner of sin, so that what was promised, being given through faith in Jesus Christ, might be given to those who believe. ²³ Before this faith came, we were held prisoners by the law, locked up until faith should be revealed. ²⁴ So the law was put in charge to lead us to Christ that we might be justified by faith. ²⁵ Now that faith has come, we are no longer under the supervision of the law. " 

Obviously there are plenty of other benefits in the law in showing the character of God and the morals required by God. But you always have to bear in mind that the law is a mirror or a gauge... it shows you what is right but gives no means of obtaining it. In fact to try just read the Bible as a book of laws and try in your own strength to go out and obey them, you will find the law a strict and condemning master. (Rom 7, 2 Cor 3) A thermometer might tell me that I have a fever, but swallowing the thermometer isn't going to cure the fever (might just cause other problems!)

So when it comes to Christians, obviously we should desire to live obedient lives to God and what He desires as shown in the law. But what is the means of obtaining such a life? In short, Paul tells us there is a new way of living a righteous life that the law was powerless to achieve. 

Rom 8:3 "For what the law was powerless to do in that it was weakened by the sinful nature, God did by sending his own Son in the likeness of sinful man to be a sin offering. And so he condemned sin in sinful man, ⁴ in order that the righteous requirements of the law might be fully met in us, who do not live according to the sinful nature but according to the Spirit. "

In regards to your objections, I'll just state a few things. As Galatians states, the whole world was a prisoner to sin. This is before and after the law was given. God created man and woman in His image and declared them 'very good'. But we made a choice to go against the command of God and sin. You and I weren't there in the garden but if we were I'm sure the result wouldn't have been any different! Yes, we all are now born with a fallen nature but that doesn't excuse our lifestyle and rebellion as you may like. We still get a choice. And we still choose to go our own sinful way. So with the whole world as a prisoner to sin, the law was given (in terms of salvation which is the most important aspect) to show mankind they needed a saviour. The biggest problem God had is not that He had a sinful creation. The biggest problem is that He had a sinful creation that was filled with pride and self confidence and didn't even see it's sin or that it needed a saviour. The law was put in charge Galatians 3 tells us to hold us prisoner so that we would be ready for a saviour. The law would lead us to Christ by showing us our need!

So no, God is not unjust in giving the law. Just the opposite. It was His mercy that did it so that we could be saved. For those that are saved, God has been merciful again in giving His Holy Spirit in indwell and strengthen those that are His. In short, God has been amazingly gracious and provided not only forgiveness, but a new way of living righteously through His Holy Spirit so that the righteous requirements of the law might be fulfilled (not by us, as in our own strength), but in us through our relationship with Jesus.

In regards to your last couple of question, the work that God now requires from mankind is this:

John 6:28-29 "Then they asked him, "What must we do to do the works God requires?" ²⁹ Jesus answered, "The work of God is this: to believe in the one he has sent."

With the sacrifice for sin already made, that is the key command of God to mankind now. If a person decides to disobey that and not rely on Jesus' payment for their sin, then on judgment day they will have to pay for their own sin. No one will be able to say "I'm just an unfortunate handicap" as you say. Judgment will be made on the basis of something that was well within their grasp: To believe in the Son of God.

John 3:16-18 "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. ¹⁷ For God did not send his Son into the world to condemn the world, but to save the world through him. ¹⁸ Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God’s one and only Son."

All the best