I'm not convinced by any of the formal arguments I've seen against computationalism and I don't think neural networks are any different in what they can accomplish logically from von-Neumann computers (after all, hardly anyone builds neural networks - they just simulate them on conventional computers because its easier).Because I've just spent a year studying the philosophical foundations of cognitive science and computationalism is as dead as the dodo. It is history. It went the same way as behaviourism, it's just some remnants of the computationalist rump (the slow ones) haven't yet cottoned on to the fact that it is in indeed dead. Connectionism delivered the first blow. Searle, Jackson and the "emobodied cognition" crew finished off the job. Computationism is dead. Let it rest in peace.
Having said that, the idea of "embodied cognition" (as explained here http://www.iep.utm.edu/e/embodcog.htm) does seem to make a lot of sense. What puzzles me is why you think it is incompatible with materialism? The whole thing seems a lot more physically-grounded and less etherial than viewing cognition as computation.
If cognition isn't associated with a particular physical phenomenon (like computation) but is an umbrella term for a range of quite disparate concrete behaviours undertaken by organisms (or potentially machines) then perhaps there is no single, non-physical thing called "mind" that requires explanation? Perhaps we have created a mystery for ourselves by trying to find a single answer to a bunch of quite different questions?