To be descended from something, at some point, you have to be able to interbreed with the something, and we could no more interbreed with neanderthals or any other hominids, than we could with horses or chickens. In fact the lack of crossbreeding was always a big mystery, and the DNA studies pretty much cleared the mystery up.
There are a couple of errors in your post.
You are correct that Neanderthal is not an ancestral species. A lot of folks figured that out a while back, and the mtDNA has just confirmed it.
But there is no reason to believe that Neanderthal was "the closest thing to a modern human amongst the hominids." There is a nice progression going back through a succession of archaic humans (see the nice skulls at the bottom of the post) to the earlier Homo species and back to the Australopithecines (see the chart in my previous post; #246 I think).
Your statement "All other hominids were further removed from us THAN the neanderthal, and that includes homo ergaster and all the rest" does not coincide with what I have learned, and I can't accept it without some documentation. (And please, no creation websites. Their "science" is simply not science. They are the last ones people should trust when it comes to evolution, not the first.)
About the interbreeding and crossbreeding. I think you have a confused notion of evolution and how it works. You don't have a dinosaur getting a fever and suddenly giving birth to a bird. That's an inaccurate creationist strawman.
Each generation is almost exactly like the previous one, and there is no trouble with interbreeding. The key is almost--you are not the same as either of your parents, and I believe will have picked up four or so mutations besides that. So, we have microevolution in just one generation; we have it in every generation.
Add a million or ten million years and there is no reason to expect that some species undergoing environmental or other stresses will not have added sufficient change to amount to macroevolution, that is, a change from their ancestors sufficient to be considered a new species.
Finally, do you have a reference for "Neanderthal DNA is described as "about halfway between ours and that of a chimpanzee"? I have not seen that and doubt its accuracy.
Herto skulls (Homo sapiens idaltu) Some new fossils from Herto in Ethiopia, are the oldest known modern human fossils, at 160,000 yrs. The discoverers have assigned them to a new subspecies, Homo sapiens idaltu, and say that they are anatomically and chronologically intermediate between older archaic humans and more recent fully modern humans. Their age and anatomy is cited as strong evidence for the emergence of modern humans from Africa, and against the multiregional theory which argues that modern humans evolved in many places around the world.