It might be a little too late for me to chime in on this, but I was able to somewhat sound dampen a room on the cheap, starting with picking the right room to use. My newbie attempt involved...
-I picked a basement room, in a corner so two of the walls (and floor) were solid to begin with.
-I stuffed the other two walls with "safe n sound" insulation and then put up two layers of sheetrock on them.
-I separated the sheetrock layers with rubber pads every 2 feet, so I gave the wall a semi-floating/absorbing effect - or so I like to think.
-I bought a thick floor pad, on which I put thick hardwood floors
-I stuffed the ceiling with two layers of 'safe n sound', blocked the air vent, and then put up a couple layers of fabric to hold it all in place and to keep it looking nice (fireproof fabric). Adding sheet rock instead of fabric would of added more sound proofing, but that wasn't my main goal.
-I went crazy with the foam hole filling gun, blocking all holes.
-put up a heavy door, with weather striping.
-added sound panels and bass traps to the walls.
-added a rug.
I still get a bit of deep bass getting into the room when playing loud music in the room above it, or when someone stomps by upstairs, but with the door shut its a hell of a lot quieter than when I started.
I really wouldn't think Styrofoam would be good for sound proofing but i can see it useful for absorbing some structural vibrations. Heavy materials = better. Lead walls would be perfect!