We investigate the dynamics of cell signaling using an experimentally based Boolean model of the human fibroblast signal transduction network. We determine via systematic numerical simulations the relaxation dynamics of the network in response to a constant set of inputs, both in the absence and in the presence of environmental fluctuations. We then study the network's response to periodically modulated signals, uncovering different types of behaviors for different pairs of driven input and output nodes. The phenomena observed include low-pass, high-pass, and band-pass filtering of the input modulations, among other nontrivial responses, at frequencies around the relaxation frequency of the network. The results reveal that the dynamic response to the external modulation of biologically realistic signaling networks is versatile and robust to noise.