"That, IMO, is the problem. If you'd argue that species change/mutate within themselves, then I'd agree. But it's the idea that monkeys BECAME people (ie. one kind of DNA turning into another kind of DNA) that disproves Darwin's theory for me (and, I suspect, more and more scientists as more is learned about biology, DNA, etc)."
First, let me say that the definition of the word "species" is a little "wishy washy" in my opinion. It is applied different ways at different times. Generally it refers to organisms that have become SO DIFFERENT, that they have lost the ability to reproduce between themselves. Sometimes this means that they are genetically incapable of producing offspring, sometimes it means that behaviorally they do not produce offspring. Point being, "species" can seem and often is, rather an arbitrary point on a continuum between point A and point B.
The donkey and horse are a good example of "borderline", they are similar enough to produce a mule when you cross them, but are different enough that the offspring is "not quite right", its sterile.
Species do not "pop" into existence (although some features might like new flower color for example), they are the result of generations of changes.
I'm forgetting the name of the species (I'll look it up if someone REALLY needs to know), but there is a bird, a type of seagull as I recall, that is found all the way around the world. If you compare one population to the population a little east of it, they are slightly different, but without doubt the same species. By the time you follow the loop all the way around the world and the extremes of the two ends meet, they are so different, that they do not interbreed.
If the intermediate populations were to die out (comet, volcano, disease, whatever), these would without doubt become considered two species. They are just NOT the same bird. It is only the existence of a continuum from point A to point B that allows these birds to be considered the same species.
Actually the two ends of the loop: The Herring Gull (Larus argentatus) and Lesser Black-backed Gull (L. fuscus), are considered to be two species, because that's how they are where their habitats overlap in the British Isles.