Biochemical reactions in cells occur in an environment that is crowded in the sense that various macromolecular species and organelles occupy much of the space. The effects of molecular crowding on biochemical reactions have usually been studied in the past in a spatially homogeneous environment. However, signal transduction in cells is often initiated by the binding of receptors and ligands in two apposed cell membranes, and the pertinent biochemical reactions occur in a spatially inhomogeneous environment. We have studied the effects of crowding on biochemical reactions that involve both membrane proteins and cytosolic molecules by investigating a simplified version of signaling in T lymphocytes using a Monte Carlo algorithm. We find that, if signal transduction occurs on time scales that are slow compared to the motility of the molecules and organelles that constitute the crowding elements, the effects of crowding are qualitatively the same as in a homogeneous three-dimensional (3D) medium. In contrast, if signal transduction occurs on a time scale that is much faster than the time over which the crowding elements move, then the effects of varying the extent of crowding are very different when reactions occur in both 2- and 3D space. We discuss these differences and their origin. Since many signaling reactions are fast, our results may be useful for diverse situations in cell biology.