Philosophy of the Mind is much different from Artificial Intelligence. And it is also much different from Neuroscience.
Neuroscience asks 'How does the Brain work?' (Based in biology and chemistry).
Artificial intelligence asks 'How do I simulate human intelligence?' (Based in math, and computer science, complexity theory).
Philosophy of the mind asks a lot of messy questions that don't really fall into either of those buckets. The mind isn't the brain, and the mind isn't strictly human intelligence, so what is it?. What is consciousness? How is it that I have an idea of self? What are my perceptions? How do I model the world around me? What's up with free will?
It is as much about asking these questions and refining them into new questions, as it is about anything else, and most of these questions really can't be answered with scientific facts or mathematical algorithms.
From the aspect of learning philosophy in a historical context, you kind of have to, otherwise you are sort of doomed to repeat the mistakes of others who came before. In stark contrast to science, in philosophy, you are questioning the nature of reality. Hence you cannot really design experiments (unless you are G.E. Moore), to prove this or that philosophical property. Instead, you have to build on all of the other work that has come before you, and understand why the things that people thought were true, are untenable or not true.
(rather long unrelated tangent: A number of people, like pg, think this is kind of stupid. The other options, unfortunately, are chasing our tails, or simply saying that these questions are unanswerable. Sometimes, Wittgenstein is interpreted as saying that all philosophical questions are simply reduced to 'language games'.My interpretation is more that he is making a statement about the relationship between reality and language, we are using language do describe reality, but there are certain things which contain the reality which cannot be described with language, because language is a part of that reality. There is a very strong parallel between his work and Godels'.)
So no, philosophers do not ignore science. But a lot of the time, when something has been solved by science, philosophers stop worrying about that realm so much. (Why use philosophy where you can use objective fact?)
Another example is that philosophy is very firmly ingrained in things like string theory or quantum mechanics. But the truth is, string theory and quantum mechanics boil down to equations which describe things that we have already observed. You still need a discipline in which you can speculate and say, 'Ok, but what does this mean about the nature of my reality? How does this effect me beyond being interesting math? What is the implication here?'
And that is what philosophy does.