We report nonlinear measurements on 80µm silicon photonic crystal waveguides that are designed to support dispersionless slow light with group velocities between c/20 and c/50. By launching picoseconds pulses into the waveguides and comparing their output spectral signatures, we show how self phase modulation induced spectral broadening is enhanced due to slow light. Comparison of the measurements and numerical simulations of the pulse propagation elucidates the contribution of the various effects that determine the output pulse shape and the waveguide transfer function. In particular, both experimental and simulated results highlight the significant role of two photon absorption and free carriers in the silicon waveguides and their reinforcement in the slow light regime.