  We numerically obtain the full time-evolution of a parametrically-driven
dissipative Bose-Einstein condensate in an optical cavity and investigate the
implications of driving for the phase diagram. Beyond the normal and
superradiant phases, a third nonequilibrium phase emerges as a manybody
parametric resonance. This dynamical normal phase switches between two
symmetry-broken superradiant configurations. The switching implies a breakdown
of the system's mapping to the Dicke model. Unlike the other phases, the
dynamical normal phase shows features of nonintegrability and thermalization.
