Why the Qur'an affirms the Bible, and the problem that poses for Islam

Surah 6:115
The word of thy Lord doth find its fulfillment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.

Notice that it does not say "No one can change the Qur'an," but "None can change His words." That is, if Alllah has revealed words which are not the Qur'an, those are still the words of Allah.

Surah 18:27 backs this up perfectly:
And recite (and teach) what has been revealed to thee of the Book of thy Lord: none can change His Words, and none wilt thou find as a refuge other than Him.

Again, "None can change His Words," not "None can change the Qur'an." This is talking about all of the words of Allah, not just the Qur'an.

So when we look at Surah 3:3
It is He Who sent down to thee (step by step), in truth, the Book, confirming what went before it; and He sent down the Law (of Moses) and the Gospel (of Jesus) before this, as a guide to mankind, and He sent down the criterion (of judgment between right and wrong).

We are assured that since Allah revealed the Torah and the Gospel, they are Allah's incorruptible words.

Since the Torah and the Gospel are the words of Allah, they cannot be corrupted. Since the Gospel says that Jesus died, and the Qur'an says that Jesus didn't die, then Allah is wrong. Since Allah is wrong, Islam is false.

Feel free to look these references up yourself.

Now, why do I believe that the Bible I have today is the Gospel Muhammad was talking about?

Very, very easily. We have copies of the New Testament which predate Muhammad by 300 years. We know exactly what the Gospel was in Muhammad's day. It was exactly what is recorded in our Bibles today.

The Gospel that was around in Muhammad's time is exactly the same Gospel we have today. If Muhammad wanted to say that it was corrupted, he did a very, very poor job of it. In fact, Muhammad told the people to judge by the books they had between their hands... that is, Muhammad affirms the Torah and the Gospel as they existed in his day.

So if Muhammad is right, Allah is wrong. And if Allah is right, Muhammad is wrong. And either way, Islam is false.