OK. If this it true then maybe by definition speciation has been observed and I was wrong. My contention all along is that we haven't seen evolution according to the old school definition. What your talking about is a new population of fruit flies, or resistant bacteria. I'm talking about something entirely new like the difference between a frog and a bat. They both eat insects but they couldn't be more different. Anyway, I know that you would respond that is not what evolution is. True, but 90% of the world thinks it is. (I'm guessing)
But here is what you seem to be missing. Two new populations of fruit flies -In different environmental niches will be subject to different selection factors. This ultimately means that gene flow is no longer available between the two groups and the gene pools will diverge.
Now you want to see a cat turn into a dog via evolution -Which obviously will never happen because they are of two separate lineages, but above we now have two lineages that will split off from one another and begin to collect differences over generations. Is there some quantitative amount of differences you require to see to believe evolution? Or do you know some mechanism that will stop these lineages from one day looking drastically different from one another?
You know thinking about this, I think this kind of goes back to the problem of (well the creationist problem of); Why no new phyla?
What you guys seem to be missing is that all extant life today is a living lineage. And all descendants of those extant organisms will always be part of that lineage. So you guys want to see something like reptiles turn into birds -But birds will never have offspring that are anything but birds and those offspring will always be descendants of birds. Never some other extant taxonomic grouping.
I explained this to someone over on EvC forum sometime ago, let me use my pictures from there to help (and cause my finger is starting to get sore!).
Lets pretend for a moment, we have some make believe planet (name it whatever you like). And on this planet lives a species (an ancestor to all life on the planet) we will call Bobs. The happy little black dots.

Now there is one population of Bobs, but after some amount of time something happens that causes the population to be split in half and these two new populations are reproductively isolated from each other. After some amount of time, the changes to each population (through differing selection pressures) eventually becomes so great that we call them different species; Jims and Jons.

After sometime both of these new species produce more (from left to right; Sams, Sallys, Steves, Sarahs, and Stephs)

And more(Petes, Pauls, Zachs, Rons, Robs, Rays)

Now something I forgot to include is some kind of time scale, so the farther down the page a dot or node is the later in this planets geological time it occurs.
This branching we see is an emergent property of the relationships of 'dots' in the system. We can assign arbitrary taxonomic names to nonarbitrary groupings within the tree (nested sets if you will).
Take for instance the first split from the Bobs. We have the Jims and Jons. We can call them Kingdoms, Domains, Super Cool Color Groups, whatever you want, the name is not important. What is important is that each group and all of its descendent's share some common features.
From each of these groups (Jims and Jons) arise even more groups. Again we can assign whatever name we wish (phyla for instance), the name is not important, but again the important part is that all the ancestors of the Sams, Sallys, Steves, Sarahs, and Stephs have some features common to the groups, our nested sets again.
So you ask why don't we see phyla being created still? In our example what we call phyla arose at the time of the Sams, Sallys, Steves, Sarahs, and Stephs. For more groups to arise, we would need the Jims and Jons to have another divergence. The problem is if our Jims and Jons are extinct how can that happen? Anything that arises from the Sams, Sallys, Steves, Sarahs, and Stephs will belong to one of those phyla, not a new phyla, no matter the morphological extremity. This is because, while their descendants may gain new features, these features will not be shared amongst the higher group. In other words, there is no way to travel to the past and create new forms at the level of the Sams, Sallys, Steves, Sarahs, and Stephs.
Something else you appear to be hung up on is similarity in ancestry. It can get pretty confusing to think about. But your vertebrate/invertebrate example shows that your not quite grasping it yet. Your question is why do not new vertebrates arise from invertebrates?
To answer the question, you need to first relieve yourself of the very generalized terms. Lets change your question around a little bit so that it makes more sense. Lets look at the Superphylum Deuterostome. And we can rephrase your question why can't chordates or animals with notochords arise from hemichordates (animals with primitive notochords).
After looking over the example above, the answer should come to you, but just in case lets go over it. If today, we found a hemichordate that had evolved a fully functional notochord, would that be a new phyla? The answer is no. Because this newly evolved species, is an ancestor too the original hemichordate. In other words, because it is a descendant within the group hemichordata, it cannot ever 'leave' that grouping.
There is no rule that says, a hemichordate evolving a notochord is impossible though, but as someone pointed out, billions of years of evolution have evolved living lineages that are very specialized in niches. Its like asking why don't dogs evolve into something squirrel like? Because squirrels already fill a particular niche, the chance that dogs could displace them would require some pretty astronomical happenings. And if a new niche opened up similar to one that squirrels already fill, then squirrels would likely be the best candidate to fill the niche.
This is really interesting stuff that can really be seen in the evolution of island biota.
Anyway thanks for answering the question. Are you saying the brain because it's an organ, but we use it for thinking? Please explain.
The brain is a collection of neurons -Which work by playing with chemical equilibria. The changes to varying groups of equilibria at certain times allows for emergent properties to occur, like emotion or memory. Termite mounds would be another example.
Another good example would be birds flocking. Which each bird or part, has a simple set of rules. The outcome of all of these rules acting together is very complex behavior much more than just what it's parts are capable of.