I agree, Chinatown is a good example of neo-noir.
I think what lets Brick down more than anything (and like you, frank, I think it's way too pleased with itself and up its own arse), is that it tries to put kids into an adult genre. The point of classic noir was to show how an 'ordinary Joe', who had been adhering to society's mores and expections all his life, was brought down by a shadowy underworld steeped in crime and iniquity. The Femme Fatale was always a woman of extreme sensuality, who knew exactly how to lure and trap a man for her own personal gain. Using school kids to try and create a noirish world, is pointless; they lack the experience, the depth of depravity and hedonism that characterises the characters in a noir.
There is little sense of the danger of the forbidden in Brick; it all seems too much like a kid's game. And there is certainly a lack of visual tension, which is so essential for an effective noir.
"He may look like an idiot and talk like an idiot but don't let that fool you. He really is an idiot."