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Arab muslims conquered all the Middlle East up to the eastern edge of Asia Minor in the 600 and 700's so you're really talking about a 700 year span that the Byzantines managed to keep Islam out of Europe (paradoxically, Islam lost its foothold in the west, Andalusian Spain, at roughly the same time that Byzantium finally fell).
The Turks were a different race and whole other order of military might than the Arabs and really had nothing to do with the initial outbreak of Islam or the crusades directly.
It's completely true that the city of Constantinople was crippled and left terminally weakened by the Fourth Crusade and most of the Balkans had already fallen to the Turks by the time they took Constantinople. By 1453 The Greeks were surrounded and any relief from the west would have had to fight its way through or come by sea.
The Turks were a constant threat to take Europe for another 230 years until they were finally turned back at Vienna in 1683. From then they stagnated while Europe went through the Enlightenment and entered the modern industrial age and are left now with just Asia Minor and a little bit of Europe (including the City of Constantine). This makes modern Turkey a genuine mix of Asia and the West and completely unlike the Arabs or any other group of muslims.
It wasn't until 1071 that the Turks were able to defeat Byzantine forces at Manzikert - a part of the Byzantine empire up until that time (in eastern Turkey). Constantinople was part of the Byzantine empire and did not fall to any Islamic armies (Arab or otherwise) until 1204. The Byzantine empire kept a check on Islamic expansion until the latter end of the the 13th and beginning of the 14th centuries, when the forces of Islam finally were able to control all of Asia Minor.
The Arab muslims never were able to kick out the Christians.
Also, it was the Seljuk Turks taking of Manzikert that really started the impetus for the First Crusade,