We take advantage of the polariton bistability in semiconductor microcavities to estimate the interaction strength between lower exciton-polariton and dark exciton states. We combine the quasiresonant excitation of polaritons and the nominally forbidden two-photon excitation (TPE) of dark excitons in a GaAs microcavity. To this end, we use an ultranarrow linewidth cw laser for the TPE process that allows us to determine the energy of dark excitons with high spectral resolution. Our results evidence a sharp drop in the polariton transmission intensity and width of the hysteresis cycle when the TPE process is resonant with the dark exciton energy, highly compromising the bistability of the polariton condensate. This behavior demonstrates the existence of a small symmetry breaking such as that produced by an effective in-plane magnetic field, allowing us to directly excite the dark reservoir. We numerically reproduce the collapse of the hysteresis cycle with the increasing dark exciton population, treating the evolution of a polariton condensate in a one-mode approximation, coupled to the exciton reservoir via polariton-exciton scattering processes