I said in my previous post that Europe in 800 CE was not a 'backwater', and justified it by saying that Europe was literate and urban with trade links to the rest of Eurasia that were non-trivial. At the same time, it is clear that Europe was quite poor at that time, especially in comparison to the Abbasid caliphate or China (both of which had undergone considerable strife in the preceding century, it should be pointed out). But the point isn't to understand how Europe became wealthy - the answer to that question is reasonably obvious (hint: it involves global conquest). The point is to answer the question of how Europe achieved the means to become wealthy (ie, the global conquest part). Europe's success in conquering the world didn't require prior wealth - certainly no more than any other conquest did - and I think it is still eminently reasonable to see Europe's later dominance as having some precedents in 'dark age' Europe.
There have been plenty of empires founded by relatively poor groups. Babur recorded in his memoirs that he was once reduced to a retinue of himself and two men - and both men had been trying to kill him before he offered them riches in exchange for service. The Mongols had no cities and were reportedly non-literate before their conquests, and despite the habitual extortion of 'gifts' from China, Mongolia in the thirteenth century was a poor and sparsely-populated place of around 700,000 transhumant pastoralists. While some parts of the Arab world were urban before the Islamic conquests, most Arabs lived local, tribal lives, whether as Bedouin in the deserts or fishermen on the coasts. They were so unimportant to the rest of the eastern Mediterranean world that Maurice's Strategikon, written a couple of decades before the conquests, included no information at all on Arab fighting tactics or observations on Arab life, despite its exhaustive detail on the Sassanians and other groups of the southwest Asian interior (and despite Maurice using Christianised Arabs as mercenaries!).
Portuguese success in the Indian Ocean didn't depend on Portugal already being rich, but it did depend on a string of traits that went back to so-called 'classical' and 'dark age' Europe, including literacy in Latin and vernacular languages, the preservation (in some form) of Greco-Roman geography (it's hard to set a course for Barygaza or Kottigara if you've never heard of them), and the retention of Mediterranean naval technologies, including the lateen sail. It depended on a slew of other things as well, like the presence of the compass and paper, not to mention gunpowder and steel - things that had developed elsewhere and found their way to Portugal through the zany linkages of Eurasia. And of course, the ability to write in Latin, or any language, had a long history in the Mediterranean stretching back to Egypt and Mesopotamia.
It is necessary to have a plan in order to conquer the world, and the Portuguese had one. Specifically, Afonso d'Alboquerque had one: take the major trading settlements around the Indian Ocean and you'd have the spice trade locked up tight. The main difficulty was getting to the Ocean itself, but Vasco da Gama - almost certainly following a plan developed by Bartolomeu Dias, who had sailed down the west coast of Africa in the 1480s - showed in 1498 that it was a simple matter to do this by sailing out into the Atlantic and following the prevailing winds south of the Cape of Good Hope. By 1515, d'Alboquerque had conquered Goa (in India), Hormuz (Persia), and Melaka (Malaysia), and established relations with communities in east Africa. From Melaka, he sent Antonio d'Abreu to Maluku, Indonesia, in search of the 'spice islands' themselves (it appears that Ludovico de Varthema had already ventured to the islands, although, reportedly, few people actually believed he had at the time). D'Abreu reached the Banda islands, the source of nutmeg, mace, and cloves, in 1511.
This plan did not require a great deal of money in the beginning. The Portuguese ships were light and fast, and didn't need the combined resources of an entire nation to fund them - a few investors would do, preferably royal ones. The conquerors and explorers were motivated initially by money, it appears, just as the Borjigids and Seljuks were. So they had motivation, and the ships and knowledge gave them the means. The only thing that we can't understand by looking at the history and geography of the world at this time is the Portuguese military advantage - where did it come from? How come d'Alboquerque and de Almeida managed to take Goa with so few men, and, at Diu/Chaul, defeat a coalition of navies much larger than their own with their fleet of tiny 90-foot boats? That is probably due to the cut-throat world of the Mediterranean in the late fifteenth-century, but as with the Arab, Turkish, and Mongol conquests, it's not a variable that can be easily accounted for.
I think the Portuguese would have been shaken off like fleas from the Indian Ocean if the Americas had not been discovered and conquered by other Europeans, providing a steady and powerful flow of goods and ideas to Europe. The fact that the Portuguese empire contracted so much after a century or so indicates to me that perhaps the initial European conquests would have been just another cycle in the crazy mixing of Afro-Eurasian history. It was the other plan, the one to sail to Maluku by going around the back, that had the bigger impact, largely due to the murderous power of Eurasian diseases. But the Portuguese empire was not haphazard and it wasn't an epiphenomenon of Europe's encounters with America. Both of these sets of conquests were, in some sense, the result of a plan. The plans were necessary because of Europe's geographical position on the chilly western extremity of Eurasia, far from the main sectors of activity. Little did the plague-bedraggled penniless people of Europe know, but they were in by far the best position to take advantage of the indigenous American population's Pleistocene separation from Eurasia and absence of pastoral economies. This was only revealed - with excessively awful and tragic consequences - when Colombo left for Asia in 1492.
In some sense, then, despite the fact that Europe's geography barely changed between 800 and 1492 CE (except for major programmes of deforestation and the rise of many cities), geography was partly a cause of Europe's wealth. It was indirect, naturally - but Europe's proximity to the Americas and its placement at the end of Eurasia preventing easy access to Indian Ocean trade (then the big pond with lots of big fish around it) provided part of the means and motivation to conquer most of the world.