  We numerically study the effect of adding quenched disorder in the form of
randomly placed pinning sites on jamming transitions in systems that jam at a
well defined point J in the clean limit. Quenched disorder decreases the
jamming density and introduces a depinning threshold. The onset of a finite
threshold coincides with point J at the lowest pinning densities, but for
higher pinning densities there is always a finite threshold even well below
jamming. We find that proximity to point J strongly affects the transport
curves and noise fluctuations, and observe a change from plastic behavior below
jamming, where the system is highly heterogeneous, to elastic depinning above
jamming. Many of the general features we find are related to other systems
containing quenched disorder, including the peak effect observed in vortex
systems.
