Emission dynamics of a multimode broadband interband semiconductor laser have been investigated experimentally and theoretically. Non-linear dynamics of a III-V semiconductor quantum well surface-emitting laser reveal the existence of a modulational instability, observed in the anomalous dispersion regime. An additional unstable region arises in the normal dispersion regime, owing to carrier dynamics, and has no analogy in systems with fast gain recovery. The interplay between cavity dispersion and phase sensitive non-linearities is shown to affect the character of laser emission with phase turbulence, leading to regular self-excited oscillations of mode intensity, self-mode locking, and single-frequency emission stabilized by spectral symmetry breaking. Such physical behavior is a general phenomenon for any laser with a slow gain medium relative to the round trip time, in the absence of spatial inhomogeneities.