Muslims indeed had a large share in getting europe out of the so-called "middle ages". Although, a lot of ideas and prejudgements should be abandoned. The middle ages were not the dark and unknowing times people often think of them. They had a whole different way of thinking (and I'll spare you examples and such, as it would most likely give you a wrong idea anyway). Medieval people were, in the first place, very practical people.
The Middle ages were not illiterate and intelligence forsaken, but intellectual work and such folded back onto a very small minority in the early middle ages, only to slowly spread into a wider part of the population (I'm going to refer to Elias' "process of civilisation" here). That what we call "humanism" (renaissance is meant for the art aspect of that time) is merely the city elite starting to participate in that intellectual proces and increased contacts between people due to a grown population. Thus, the "revival" as it's being percepted today is a hyperbole.
Also, there were other"renaissances", namely the karolingian and the 12th century renaissance.
Now, to reach my conclusion: What was the role of the Muslims? They held libraries that were vast, and beyond anything alike in the christian world at that time, they had a far wider and more thorough intellectual interest during the entire "medieval times" (they also had the benefits of sharing borders with Persia, Byzantium and later on India. While most of Europe wasn't that urbanised). There were places that acted like "gateways" of intelligent works. Some examples: Spain, Sicily (where Barbarossa's son was educated), Malta etc. In all these cases, the contact was with muslims, and they provided either new works, or better versions of known works (that were often summarised in compenia like Suetonius' work.
So, yes, the muslims did help with the intellectual bloom of humanism (or renaissance), but it wasn't the only responsible factor.
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Now some comments:
"Europe just got wealthier from trade and farming techniques, which allowed an academic class to develop. Sure the academics got access to classical western information preserved and copied by the muslims, but to be honest the muslim intellectuals were just as lame as the scholastic intellectuals in the renaissance. They didn't even come close to measuring up to the Greeks. The changing academic and intellectual atmosphere, in other words, was caused by the changing social organization and economic conditions of Europe. You don't have time for contemplating philosophy when you're either training for war or the clergy, or are a malnourished peasant."
Economy is one thing, but there were many other things that allowed this change. Like a grown population, accumulation of intellectual works, and many more. But it's a false argument that both scholastic and muslim intellectuals were "lame". I've read both of them, and it's stunning how advances their thinking actually is, but it's a totally different way of thinking than we have (wich is heir to the 17th century "scientific revolution"). In certain ways, they surpassed the greeks, who were rather lazy and reasonably counterproductive. One can argue that we idolise the greeks so much cause their texts managed to survive so long 
"Well the muslims enjoyed the advantage of conquering urban societies, and their culture was trade friendly. That permitted the conditions for a more intellectual-friendly society. The Europeans began to move out of the dark ages when people started to settle in towns beginning within Italy and Flanders, and a commercial society was slowly established. What's funny is that a lot of people moved to those towns to escape the nobility, rofl.
Yes, Western Europe ruralized around the time of Emperor Diocletian, and the huge cities of the Roman empire started to depopulate as people moved out in to the country. Starting with the renaissance, people were moving back in to the cities and founding new ones (though the cities weren't nearly as big as they were under Augustus)."
European cities were growing a lot sooner than the renaissance era. Most cities were founded in the 9th - 11th century, and the largest growth of the cities was in the 12 - 13th century, wich was primarily a population expantion, as a lot of new urban villages were founded in that period (referred to in the dutch historic litterature as "de grote ontginning"). Regional differences do exist, but it's undisputable that it happened before the renaissance. You seem to contradict yourself with this even Justinian. You claim that it was trade and growing cities that enabled renaissance, while you say that it was in the renaissance period that the cities actually started expanding. You are correct that an economic expantion was needed for the renaissance, but as I said briefly above, there were other renaissances as well, and what makes it them different is the increased population, and with that the larger density and unification of people and with that a lot more contact between them. That is what made the 15th century renaissance 'succesful'
God: Behold ye angels, I have created the ass.. Throughout the ages to come men and women shall grab hold of these and shout my name...
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