Max Replies, and I don't know if you all read the comments, so I'm bumping this to the front.
I think I can partially answer your question.
The 'dark ages' view is a leftover of 19th century historical thinking. Its wrong, and dismissed by modern scholarship.
First, let me define the medieval period from 800-1400CE, and the Renaissance as the long 16th century, late 1400s to mid 1600s. Most of the things I know about the shift are related to the overseas expansion. As a facet of the renaissance, there are diverging scholastic views on why the overseas expansion occurred. It seems to me as though there is sufficient evidence to point to some of the factors which caused it were from the midieval era.
Most of the scholars generally agree there is some causal relationship between historical epochs. It would be difficult to imagine the medieval era not in some way shape what would be the future. There are several modern interpretations, but no single view has emerged as dominant. Read Braudel & Wallerstein (world systems theory), Webb & Jones (frontier american crap), Mann & Hall (for a rejection of Wallerstein and Braudel) for more. There's also a Marxist interpretation that has to do with feudalism.
I'll give you one concrete economic example of a linkage between the epochs. Italian banking which emerged in the 14th-15th centuries had its roots in medieval monetary systems.
Or, the reformation, a definative portion of the Renaissance, was the result of a multitude of issues facing Catholocism in the medieval period.
Now back to Me:
This whole debate reminds me of an issue I learned about first-year relating to the new world and the slave trade: Up until roughly the 1400s, Europe, Asia, and Africa were still unequally developed, but were still largely of the same kind, differing only in degress. Indeed, China would really stay ahead of Europe in many ways until the 1700s. (China was still beating Russia in land wars up until then.)
Then comes the discovery of the New World, which was quickly vacated by western imperialism and more thoroughly by western diseases. This left a huge amount of useful land, but little labor to use it with. Enter the slave trade - the Carribean and Southern US quickly become sources of primary agricultural products to send back to Europe. More importantly, the profits from both the slave trade and the plantation colonies both accrue to Europe, while Africa's youngest and strongest are being shipped to the new world. It's not the absolute or relative numbers of Africans shipped that was important, in this reading. Rather, because it was primarily the youngest and strongest being taken, the tribal societies were destroyed.
To pull back, what you see then is a very direct influx of financial capital in to Europe, based on the exploitation (in both senses of the word) of human capital in the New World and Africa. Think of a bar graph starting (roughly) in 1400, with African, Europe, and Asian "society" represented, and all on more or less the same plane. After 1492, Asia stays still, but Africa starts to go way down while Europe's goes correspondingly higher. Actually, I'd wager this process only really takes off in the mid-1600s, but that's an uninformed opinion on my part.
Given that European immigration to the new world was relatively limited before the 1800s, it's an interesting question to speculate on: could the US have ever been built without the slave trade?
(Pet peeve Rant: Why do historians bother with "Common Era" instead of the old AD? It's still referring to the same point zero - the Christian calendar, with all it's mistakes - so why bother? Does anyone really think that using the initials AD really offends non-christians? Is this one of those near-mythical "political correctness" things my history professors always whine about?)
I sure like having comments on this blog, by the way.