Two things I can think of without experimenting or seeing your file;
Make sure the cube is 'active'. If you've figured out how to get particles to bounce off an object, then you probably remembered.
Second, check the mass of your shards. The momentum of the objects will change how particles affect the larger objects. Default weight is 1. What do particles weigh (do they even have weight?)? Try setting the weight of the shards as close to 0 as possible, and if they have it, weight of the particle up.
If that still doesn't work, try something like this; set it up so that each particle is surrounded by a tiny, invisible box (I don't know exactly how, but this should be a fairly simple expression job). With the invisible cubes set to passive, and their posistions determined by the particles, you should get nearly the same results (..... I think. I really ought to try this. I just have too many working theories).
So, umm, see if any of that works. I'd like to know if it does. Or if it doesn't, too. Anyone see holes in this?