Truth4All, your name is deceptive.
May I prelude my post by mentioning that the church of England recently released an official apology to Charles Darwin (a little late, but still a nice gesture) for condemning his ideas ages ago? This, in light of the overwhelming amount of evidence for it.
Truth4All, you are a good example of what is so detrimental to science education today. You know a little bit about evolution... Matter of fact, you know more than most. But you obviously know nothing of any substance. In cases like you, knowing a little is more dangerous than knowing nothing because you are capable of misrepresenting the facts in a way that sounds intelligent so that others who know less will believe you.
There are a lot of mistakes in your post, but before I go talking about them, I will request that you present me with a link or journal or something that supports your claim, "Modern science has discovered the barrier, an absolute barrier, beyond which a species can never go."
Now for the problems....
"Modern genetics has shown that within the gene pool of every creature is a range of possible variations, which express themselves when the environment alters. Darwin knew nothing about genes."
Apparently, neither do you. By "within the gene pool of every creature," I will assume that you mean "within the gene pool of every species." You say that within this gene pool, there is a range of possible variations which express themselves when the environment alters. Oh really? How do they "express themselves?" When an environment alters (and the environment is ALWAYS altering, especially since new viruses and diseases are constantly mutating), the organisms who have traits which help them survive live on, then procreate, passing on their genes and their mate's genes to their offspring. Consequently, the offspring now have the genes which determine these traits, and also have their own new genetic code, rendering them a challenge to the plethora of microscopic predators. This process continues until only organisms with the traits fit to the environment are left, procreating. The beak size of Darwin's finches was a response to the necessity of these finches to have harder beaks to crack open the tough seeds that were their food. Finches with softer beaks struggled to eat and died young or had weak offspring. As a result, they died off and were no longer a part of the gene pool. Over a few centuries, only the finches with genes dictating hard beaks were left.
This is how species evolve. It is a known process, understood by science, and is fully capable of being taught and understood, if only SOME PEOPLE would stop thumping their bibles and listen to some legitimate inquiry into the truth of the natural world for once. The Bible is true... but not in the sense that my science textbook is true. Genesis is a great book... But it is absolutely not a historical account of anything that ever happened at any point in history. It is highly metaphorical/symbolic and its message about lost innocence is deep. But the Bible is not a science book. Let's remember that.
"Environment and natural selection allowed the finches to adapt and change slightly, but they remain finches, and can all interbreed."
Yes, obviously. They will not all of a sudden turn into a giraffe. I don't understand how this comment in any way supports your idea that evolution is mistaken.
"The problem is, there is no known mechanism whereby information in the DNA can increase in complexity."
What are you talking about? Seriously, information in the DNA cannot increase in complexity? What does that even mean?
"It never increases, which is what it would need to do to cause a species to evolve upwards."
If I had a buzzer, I would buzz it right now. I need to correct you. Evolution is not progress. It is not "getting better." Darwin himself explicitly stated that "evolution is not progress." All it is is change in response to the environment. There is no "upward" movement (figuratively).
"Variation is not evolution. It is a selection process from already present genes. If there are no new genes to choose from, a species remains stable and is conserved indefinitely."
Nor did anyone say variation was evolution. Matter of fact, those are two completely different ideas. I think you meant that variation is not evidence for evolution (even though it is, in combination with the other evidences). Anyways, you display a vast ignorance of biology here. But I would expect that because if you did know anything about biology, you would understand evolution and we wouldn't be having this discussion. But look: there are ALWAYS new genes. Each generation of a species is a new gene pool, waiting to combine with the others and create a new one for the next generation, and so forth. As a matter of fact, the very reason that sex even exists as the mechanism for procreation is that the combination of two organisms' DNA creates new DNA in their offspring: this presents a challenge for viruses and bacteria that would otherwise quickly adapt and just attack the species with one set of DNA being passed down generation to generation. Asexual species are basically cloning themselves. There are very few species like this.
I would suggest that you take an evolution class at your local community college or just understand more about it and why creationists and Intelligent Design advocates are completely mistaken in pretty much everything they say. Evolution challenges certain beliefs, but it is a well-known fact in the scientific community and it would be wise of you to listen up.