Grain growth in a polystyrene-polyisoprene block copolymer melt is studied by time-resolved depolarized light scattering after a quiescent quench from the disordered to the ordered state. At shallow quench depths, classical nucleation and growth kinetics are observed. Grains comprising the equilibrated ordered phase nucleate and grow by consuming the surrounding disordered phase. In contrast, deep quenches result in the formation of disorganized grains with an average order parameter that is well below the equilibrium value. Small angle neutron scattering and rheological experiments were conducted to facilitate the interpretation of the light scattering data. We show that the nonequilibrium grain structure formed during deep quenches is due to extremely high nucleation density. Under these circumstances, the space required for the formation of equilibrated grains is unavailable.