Lennard Jones liquid vapor phase transition
I think your transition, if present, may be drowned out by noise, as your RDF is only produced by 108 particles. As the Lennard-Jones interaction is quite simple and you are using cutoffs (good idea!), is it possible to increase the number of particles in your simulation somewhat, or else take the mean of some large number of trials?

This said, it does not take much imagination to see a continuous PV plot from about 0.7 onwards, which might mean you have something analogous to a supercritical fluid. Maybe try a number of trials at different pressures?