It seems to me that that the whole basis of your religion revolves around the alleged crucifiction of Christ. As the Bible states in Paul I Corinthians Chapter 15 verses 13 and 14 and i quote:

13.But if there be no ressurection of the dead, then is Christ not risen. 14.and if Christ be not risen,then is our preaching vain,and your faith is also in vain.

You got that completely right. I am glad for every Muslim who has taken that much effort to read the Bible and realize this and then is courteous enough to ask for the meaning instead of attacking it as wrong before making the effort to understand it. So, you are most welcome with your questions.

Actually, the cross and the resurrection is THE non-negotiable of Christianity. The Trinity is sort of an "advanced topic", and not necessary for salvation, though the deeper meaning of the Cross will only become clear when viewed from the perspective of WHO died on this cross.

Yes, the basis of the Christian faith is the crucifixion and resurrection of Jesus Christ. Without this being a real historical event, there would be no basis for the christian faith at all. If somebody could show me conclusively that the resurrection of Jesus has not happened, then I would have to stop being a Christian immediately.

What would you have others remember about you after you are no longer with them? What would Jesus want his disciples to remember when he leaves this earth in his visible form?

Jesus the evening before he will go to the cross, tells his disciples to remember him in a very specific way.

Jesus institutes the "Lord's supper" and says the disciples should remember his death. At this moment, he does not focus on his miracles, on his virgin birth, on his teachings or anything else. He makes clear, that he wants to be remembered for his death and that this death is for the forgiveness of sins.

Let me quote Jesus (from Luke 22):
15   And he said to them, "I have eagerly desired to eat this Passover with
     you before I suffer.
19   And he took bread, gave thanks and broke it, and gave it to them,
     saying, "This is my body given for you; do this in remembrance of me."
20   In the same way, after the supper he took the cup, saying, "This cup is
     the new covenant in my blood, which is poured out for you.

What is this new covenant about? Among other things:

  The time is coming, declares the Lord, when I will make a new covenant...
  ... For I will forgive their wickedness and will remember their sins no more.
                                                       Jeremiah 31:31.34

Jesus gives his mortal body and his blood for the forgiveness of sins. And as repeated over and over again in the Old and New Testament, "without the shedding of blood there is no forgiveness". (e.g. Leviticus, Hebrews). The penalty for sin is death, and the death of the animal in the old covenant is a symbol of the death of the one righteous one who will pay the penalty once and for all in the new covenant. [That is by the way the reason that Christians do no longer sacrifice animals]

The sacrificial death, THAT is what Jesus wants us to rememeber, because THAT is what he has come for. That is the most important thing on Jesus mind. And he had spoken about this time and again earlier already, not just before he dies.

  The Son of Man did not come to be served 
  but to serve and give his life as a ransom for many.
                                   Mark 10:45

Please dont get me wrong, it is established as an article of faith amongst Muslims to believe in Jesus christ as being one of the mightiest messangers of God. We believe that he performed many miracles,by Gods permission,including healing the blind and giving life back to the dead. We do not, however, believe that Jesus is the son of God. Having started to study the Bible, in particular with reference to the crucifixtion of Christ which,as i have said earlier seems to be the whole basis of your religion. Putting aside the authenticity of the Bible for a moment and assuming that it is accuarate. There still appear to be many evidences that indicate that Jesus did not die on the cross and was not ressurrected from the dead.As a Muslim i believe that man has to bear the consequences of his own sins and that no one can bear anothers burden because this would not be in keeping with the justice that we attribute God with.This is also mentioned somewhere in your Bible the verse escapes me for the moment but reads something like

The soul that sinneth he shall die and the son shall not bear the inequity of the father......

Yes, that is in Ezekiel 18:4 & 20 and more such verses.

But note: Jesus is neither the father of any earthly person nor does he have an earthly father so that strictly speaking even if he does bear the sin of the whole world, he does not violate this verse. The meaning of this verse [against the complaints of the Jews that they are unjustly punished for the sins of their forefathers] is that God does clarify that nobody will be punished for the sins of other people, and everybody will be responsible his own sins.

Now, this does not exclude, that somebody will voluntarily step into the gap and take up the debt of others. It only says, nobody will be forced to bear others' sins.

Is the solution the Bible presents against justice? It is justice and mercy meeting each other. No transgression is "just dismissed", all sin receives its penalty, but if mercy steps in and takes over the penalty for you, will you really complain?

I think there is NO sound evidence (in the Bible) for Jesus not having died and risen from the dead. But that is discussed elsewhere, so I leave that one alone, especially as you have graceously asked "under the assumption of the accuracy of the Bible". :)

More material on this topic can be found at these pages: