We develop a generalization of the Rouse model for the dynamics of a flexible, linear macromolecule. This dynamically disordered Rouse (DDR) model is based on a Smoluchowski equation for bead coordinates, in which the bead mobilities are stochastic variables which fluctuate between zero and a finite value. The DDR model may be regarded as a generalization of previous extensions of the Rouse model with nonuniform but time-independent bead mobilities to the case in which the mobilities of the beads are allowed to fluctuate. We focus on the contribution of intrachain relaxation processes to the viscoelastic shear modulus, G(t), of a macromolecular fluid. In the limit of rapid medium fluctuations, we recover for G(t) the prediction of the conventional Rouse model. For a slowly relaxing medium, G(t) is characterized by an initial decay, followed by a plateau, and a terminal decay regime exhibiting renormalized Rouse behavior, in qualitative agreement with the shear modulus of dense polymer fluids at short and intermediate times. The center-of-mass diffusion constant displays a crossover from the Rouse result to behavior controlled by obstacle relaxation as the lifetime of medium fluctuations is increased.