Efficiently computing or approximating the VC-dimension of a neural network
If you are willing to constrain the problem further by letting the network be layered, then Tom Mitchell's "Machine Learning" gives an upper bound of ( $2ds \log(es)$) (section 7.4.4) where $s$ is the number of internal nodes (which must be higher than 2), $d$ is the VC dimension of the individual nodes, and $e$ is the base of the natural logarithm. If you're after a bound on the number of training examples then this information should be enough.

It's not strictly an answer to your question, but it might help you on the way. The result is due to Baum and Haussler (1989).