How can I make a particle system where particles don't emit light ?
Particle systems don't emit light by default, only if you add an emission material to it.
That looks like a Halo particle system, which renders as "blurred dots" in Blender internal.
Try disabling the Halo option under the Properties Editor > Particles > Render > Halo to something else like an object or group.
Alternatively add a new material to the object, set it to Halo type and assign it to the Particle System under Properties Editor > Particles > Render > Material menu. Control it's settings to match whatever effect you desire.