The Logical Contradiction at the Foundation of Islam.
Islam claims that Allah is also the God of the Old Testament and the God of the New Testament. There are over 120 references to the Scriptures of the Jews and Christians testifying that they are a genuine revelation of God (see Q 2.136, 4.163, 10.94). Muhammed did not claim to bring a completely new revelation or religion, but he thought he was bringing his people back to the religion revealed by God to all the previous prophets. For Islam to have credibility it needs to claim that it is in the line of Divine revelation, part of God's progressive revelation, so that just as the New Testament agrees with, builds on and fulfils the Old-Testament, so Muhammed claimed that the Koran agrees with and develops the previous revelation of God.
He saw Islam not as a new religion, but as the final fulfilment of Judaism and Christianity.

Muhammed thought his revelation agreed with the Bible.
In Q 10.94 he says: "If thou wert in doubt as to what We have revealed unto thee, then ask those who have been reading the Book from before thee."
The Koran therefore encourages Muslims to read the Bible as a true revelation from God. However any Muslim who does actually read the Bible or consults a true Christian will discover that the Koran
 fundamentally contradicts the Bible. The reason Muhammed did not realise this is that he was illiterate and so did not read the Scriptures himself. His knowledge was limited to what he heard from various Christian and Jews, not all of which was accurate. This explains the various errors and confusions in his retelling of Bible stories.

Basic Contradictions:
1. The Koran denies the Deity of Christ (that He is the Son of God) and the Tri-unity of God (Father, Son and Holy-Spirit) revealed in the New Testament. Q 112, 3.59, 4.171, 4.48, 5.116, 19.34,35, 6.101-6. It seems Muhammed (wrongly) thought Christians believed the Trinity was 3 gods to be worshipped: Father, Mother (Mary) and Son. See my article on Jesus - the Son of God to see how this revelation is central to the New Testament and how believing it is essential for salvation.

2. The Koran denies the crucifixion, death and resurrection of Christ which is central to Christianity and God's Plan of Salvation (Q 4.156-158).

3. The Koran contradicts the New Testament teaching of salvation by grace through faith in Jesus Christ (trusting in Christ alone as God's Son and His work on the Cross) and instead teaches salvation by works, so that at the last day Allah will weigh your good works against your sins to see if you deserve to go to heaven or hell.

The whole New Testament is about the Person of Jesus Christ, His death and resurrection and the resulting New Covenant Salvation by grace through His Blood. Take that away and you have nothing.

So there is a fundamental problem at the foundations of Islam. It claims to be a revelation consistent with the previous revelations of God in the Bible, the next stage of God's ongoing progressive revelation, but this is impossible for two reasons:

(1) The New Testament claims to complete the canon of scripture. It contains the full revelation of Coming of the Messiah, the Son of God, who came to bring eternal salvation. The Old Testament had all looked forward to His Coming, and so by its very nature it was incomplete and required fulfilment in the New Testament through the Coming of Christ. But now that Christ has come and fulfilled the Old-Testament and has provided a perfect salvation, God has nothing more to add. In Christ everything is fulfilled and through Him all things will come to their fulfilment. If we reject Christ as God's Son then we also reject God and His salvation (1John 5:11,12). There is nothing greater than Christ. Anything else would be an anticlimax! God has spoken through the prophets and now He has spoken His ultimate word through His Son who is the perfect revelation of God and brought in the perfect covenant for our salvation and union with God (Matthew 5:17, Hebrews 1, Revelation 22:18,19).
Therefore any further revelation beyond the New Testament is not of God.

(2) More than this the Koran actually contradicts the New Testament at all of the most important points of doctrine. Does God contradict Himself? No!
Therefore the Koran can't come from the same Divine Author as the Bible.

After a time Islamic scholars who actually read the Bible began to realise this problem. In his ignorance of the Bible, Muhammed claimed his verses agreed with the Scriptures, but in fact they greatly contradict what God had revealed previously. The only honest conclusion when faced with these contradictions is that either the previous revelation in the Bible are not from God, or else that the Koran is not a genuine revelation of God. But either of these options would be contrary to the plain teaching of the Koran and would therefore undermine Islamic belief.

So how could they explain this internal inconsistency? They made a claim that is demonstrably false, yet they proclaim it with conviction because, to them, it has to be true otherwise Islam is false! They claimed that the Bible has since been greatly corrupted and that is the reason it differs from the Koran. Therefore only the Koran is trustworthy. Since then, every Muslim is told this falsehood and they are quick to accept it without question and pass it on, so that it has become an Islamic myth.

However if they considered the excellent manuscript evidence for the Bible they would see there is no basis for this claim, for we have complete manuscripts of the New Testament from over 200 years before Muhammed (who lived in ~600 AD)! In fact there are thousands of manuscipts of different portions of the New Testament from well before Muhammed's time, and although there are some minor variations none of them affect any important doctrine. Therefore we know for certain that the Bible we have now is substantially the same as the one used in Muhammed's time, which He affirmed as a genuine and accurate revelation of God - it simply has not been corrupted as Islam claims. So his claim that the people of his time would find his revelations to be in agreement with the Books possessed by the Jews and Christians is manifestly false. In fact, they are opposed to most of the main teachings of the Bible.
If the Bible is a true revelation of God then the Koran is false, and if the Koran is true the Bible must be false. But what can't be true is what the Koran claims, namely that they are both from the same God, with the Koran being just a further development of the earlier revelation. Therefore the Koran is wrong.

If a Muslim ever came to face the manuscript evidence of the Bible, he would have to admit
that there is a contradiction at the heart of Islam, and therefore serious errors in the Koran. The fact is that the Koran fundamentally contradicts the New Testament that have today, and we also know from complete manuscripts 250 years older than Islam, that the New Testament  has been preserved uncorrupted, so that the New Testament used in Muhammed's time was fundamentally the same as the one we have today. Yet in the way the Koran retells many stories about Jesus and other Biblical characters, it was clearly written intentionally to be a development of the earlier Divine revelation in the Bible, and moreover it directly claims to be in agreement with it.

Since the Koran claims to be a new revelation from God it must be tested against what God has already revealed. Any new revelation of God must agree with and build upon and fulfil the previous revelation. For this reason the New Testament is diligent to document how it connects with and fulfils the Old-Testament. Thus the crucial test for the Koran is whether it agrees with the New Testament revelation.
Muhammed himself proposed this test in Q 10.94, believing that the Koran he was writing would be found to be in fundamental agreement with the Old and New Testaments. He accepted the principle that in order for any revelation claiming to be from God to be credible, it must agree with what He had previously revealed in the Bible, and that he was the latest (and greatest) in a long-line of prophets. However as we have seen the Koran fails this test and therefore it is not the revelation from God that it claims to be. It must therefore be rejected as a false revelation.

Yes, the Koran agrees with the Bible that there is one God. However, when you study the nature and character of the God of the Bible and the Allah of the Koran, you have to conclude they are not the same God. The Allah of the Koran is not the same as the God of the Bible. Likewise the Koran honours Jesus as a prophet, but dishonours Him by saying He is a mere man and not the Son of God. The Koran teaches a different Jesus. Moreover, the Koran preaches a different Gospel of Salvation (legalistic works, rather than grace through Christ). Therefore it altogether comes from a different spirit than the Bible. The New Testament strongly warns us against receiving any revelation which preaches a different gospel of a different Jesus from the New Testament for we will also then we receiving a different spirit from the Spirit of God, and the result will be our eternal destruction (see 2Corinthians 11:4, Galatians 1:6-9).