We consider a model dense colloidal dispersion at the glass transition, and investigate the connection between equilibrium stress fluctuations, seen in linear shear moduli, and the shear stresses under strong flow conditions far from equilibrium, viz., flow curves for finite shear rates. To this purpose, thermosensitive core-shell particles consisting of a polystyrene core and a cross-linked poly(N-isopropylacrylamide) shell were synthesized. Data over an extended range in shear rates and frequencies are compared to theoretical results from integrations through transients and mode coupling approaches. The connection between nonlinear rheology and glass transition is clarified. While the theoretical models semiquantitatively fit the data taken in fluid states and the predominant elastic response of glass, a yet unaccounted dissipative mechanism is identified in glassy states.