There is no original copies because it's 2000 years old and written on papyrus. There are only copies.
Likewise the Quran has no originals only copies. The paper just doesn't last that long.
Question: If there is no original copy of the Gospel (Ingeel) or the Torah, what was the point of Jesus preaching if it wasn't preserved for even 100 years.
Jesus son of Mary came to his people, to call them back to the true way of worshipping God Alone and to shun all false deities, that was the message of all the prophets of God.
i.e. And according to Muslims, who say that Paul deviated from the teachings of Jesus (introduced the trinity) ?
Maybe because Jesus son of Mary never called people to worship him? :?
We have fragments of some early copies maybe original copies from 150-200AD.
With a whole solid link of narration linked back to the time of Jesus son of Mary?
I would like to comment about why is their distrust between the people of the book and Muslims ?
I believe the teachings of the Quran contradict not only a vast number of hadiths, but itself too (explained away as abbrogation) and just plain contradiction.
That's ignorance on your part, since we know that the Qur'an and Sunnah are equal in matters of law in Islaam. So even if an authentic narration was to be a source of law, even if it wasn't from Qur'an - we still take it as a source of law since Allaah says in the Qur'an:
It is not fitting for a Believer, man or woman, when a matter has been decided by Allah and His Messenger to have any option about their decision: if any one disobeys Allah and His Messenger, he is indeed on a clearly wrong Path.
[Qur'an 33: 36]
By the Star when it goes down,-
Your Companion is neither astray nor being misled.
It is no less than inspiration sent down to him:
He was taught by one Mighty in Power,
[Qur'an Al-Najm 53: 1-5]
Some hadiths that do contradict the Quran are followed by some people, unaware of their status that are very dangerous, teaching others to kill for blasphemy, or for insulting a muslim or Muhammad, etc..
Let's see the christian stance to blasphemy:
Deuteronomy
Chapter 13
KJV
1 If there arise among you a prophet, or a dreamer of dreams, and giveth thee a sign or a wonder, 2 And the sign or the wonder come to pass, whereof he spake unto thee, saying, Let us go after other gods, which thou hast not known, and let us serve them; 3 Thou shalt not hearken unto the words of that prophet, or that dreamer of dreams: for the LORD your God proveth you, to know whether ye love the LORD your God with all your heart and with all your soul. 4 Ye shall walk after the LORD your God, and fear him, and keep his commandments, and obey his voice, and ye shall serve him, and cleave unto him. 5 And that prophet, or that dreamer of dreams, shall be put to death; because he hath spoken to turn you away from the LORD your God, which brought you out of the land of Egypt, and redeemed you out of the house of bondage, to thrust thee out of the way which the LORD thy God commanded thee to walk in. So shalt thou put the evil away from the midst of thee.
6 If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, which is as thine own soul, entice thee secretly, saying, Let us go and serve other gods, which thou hast not known, thou, nor thy fathers; 7 Namely, of the gods of the people which are round about you, nigh unto thee, or far off from thee, from the one end of the earth even unto the other end of the earth; 8 Thou shalt not consent unto him, nor hearken unto him; neither shall thine eye pity him, neither shalt thou spare, neither shalt thou conceal him: 9 But thou shalt surely kill him; thine hand shall be first upon him to put him to death, and afterwards the hand of all the people. 10 And thou shalt stone him with stones, that he die; because he hath sought to thrust thee away from the LORD thy God, which brought thee out of the land of Egypt, from the house of bondage. 11 And all Israel shall hear, and fear, and shall do no more any such wickedness as this is among you.
So if someone blasphemes in christianity and judaism - they get stoned to death!
The stories or more accurately, summaries are lacking in moral significance for the reader. It mainly teaches about the existance of God, law and how Muhammad dealt with his persercuters (unbelievers).
Very, very harshly in some cases. Compared to the detailed moral stories in the Bible, the Quran and hadith are very obviously not divine. The Quran is the equivalent of a gnostic sayings gospel.
You really think so? Seriosly, i can easily bring you a whole list of whats mentioned in the OT.
God's final Messenger, Muhammad (peace be upon him) fought those who fought the muslims, yet he inclined to peace many times, an example is when he opened Makkah and freed and forgave his persecutors and those who tortured the muslims severely throughout their lives, yet the custom at that time was to take everyone as a slave.
It brings back the concept of judging others from the law it teaches.
When Jesus main teaching was "Do not judge others, or you will be judged".
This is concerning capital punishment, which Muhammad was all for.
The Prophet said:'Do not search for (the faults of others), for if anyone searches for (others) faults, God will search for his.' (Sunan Abî Dawûd)
Capital punishment is in the OT, and since Jesus son of Mary never came to abrogate that law - it means that he was for it aswell. 
Judging others, puts love aside and teaches hate and hypocrisy. Since we all sin. We all have our failings. How is one failing better than another failing to God ? It's not, all sin is wrong.
It's men who see some crimes as worse than others, since some cause more damage to us than others.
Yeah, so if some guy comes to you and kills all your women and children, along with all your brethren in faith - you're just going to turn the other cheek right?
In Islaam - we have justice, so we can actually defend ourselves and fight back, yet Allaah does not love the transgressors.
Fight in the cause of Allah those who fight you, but do not transgress limits; for Allah loveth not transgressors. [Qur'an 2:190]
So I see Muhammad's teachings as very human. Not divine.
Religion is infact for humankind.
So a religion that is based on following the actions of a man is not a very good example to others.
So religion depends upon faith totally? No concept of being responsible for ones own actions?
The example of this man Muhammad as outlined in the Quran and hadith is not a rosy picture. Sure most of the Quran has nice teachings but there are many teachings which are very wrong, which extremists obviously follow that part of the Quran and hadith.
Maybe its because you visit anti-islamic sites alot?

How about actually reading the biography of Muhammad (peace be upon him) to really see what his life was about?
http://www.islamicboard.com/prophet-muhammad-p/1715-biography-prophet-muhammad-saws.html
http://www.islamicboard.com/prophet-muhammad-p/13954-what-non-muslims-say-about-muhammad-s.html
There is distrust because Muslims follow an example that teaches very human teachings which lead to violence and disrespecting the country they are a citizen of (bad mouthing, Sharia is better, Muslims are better than Christians, Jews, Atheists, etc).
Some of the Companions once asked the Prophet (peace be upon him) to pray to Allah to invoke His curse upon the pagans. He replied: “I was not sent to curse people but as a blessing. (Sahîh Muslim)
O mankind! We have created you from a male and a female, and made you into nations and tribes, that you may know one another. Verily, the most honourable of you with Allâh is that (believer) who has At-Taqwa [i.e. one of the Muttaqûn (pious - see V.2:2). Verily, Allâh is All-Knowing, All-Aware.
[Qur'an 49:13]
[SIZE=-1]Taqwa: piety, "God-consciousness." Taqwa involves constant awareness and remembrance of Allah, and conscious efforts to adhere to His commandments and abstain from whatever He has forbidden.
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Character, Etiquettes and Morals
[*]The Prophet said: 'Surely I was sent to perfect the qualities of righteous character (Musnad Ahmad, Muwatta Mâlik)
[*]The Prophet said: 'There is nothing which is heavier upon the balance than the good character.' (Musnad Ahmad)
[*]The Prophet said: 'Righteousness is good character, and sin is what makes you uncomfortable inside and you would not like other people to find out about.' (Sahîh Muslim)
[*]The Prophet said: 'The Muslim does not slander, curse, speak obscenely, or speak rudely.' (Sunan At-Tirmidhî)
[*]The Prophet said: 'Whoever is deprived of gentleness is deprived of all good.' (Sahîh Muslim)
[*]The Prophet said: 'Indeed Allah is gentle and loves gentleness, and gives due to gentleness that which He does not give to harshness.' (Sunan Ibn Mâjah, Sahîh Ibn Hibbân)
[*]The Prophet said: 'Whoever suffers an injury done to him and forgives (the person responsible), Allah will raise his status to a higher degree and remove one of his sins.' (Sunan At-Tirmidhî)
[*] The Prophet said: 'Do not be people without minds of your own, saying that if others treat you well you will treat them well, and that if they do wrong you will do wrong. Instead, accustom yourselves to do good if people do good and not to do wrong if they do evil.' (Sunan At-Tirmidhî)
[*]The Prophet said: 'Show mercy to those on earth so that He who is in heaven will have mercy on you.' (Sunan At-Tirmidhî)
more:
http://www.islamicboard.com/userpage-user49.html
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Note:
Not meant to be an attack on Muhammad or Muslims. Just my opinion of reasons why Jews and Christians don't trust Muslims.
We trust individual people (Muslims, Chrsitians, whoever), but I believe the agenda of Islam (Umah) to turn everybody into Muslims (all countries to follow Sharia) is absolutely wrong.
Also the idea that following Sharia will lead to less crime. Which I don't think can be possible without the expense of basic human rights and freedoms.
Is worrying. +o(
YEh
Let there be no compulsion in religion: Truth stands out clear from Error: whoever rejects evil and believes in Allah hath grasped the most trustworthy hand-hold, that never breaks. And Allah heareth and knoweth all things. [Qur'an 2:256]