Fire retardant cardboard? Most new homes in my area use shredded cardboard and paper for attic insulation .
At my work the computer racks come in half to three quarter inch thick fire retardant cardboard. I have found it to be excellent for both sound and heat insulating.
When I first moved in to my house I put in hours of sweat equity and my children grew vary board very quick. My quick remedy was to build them a zero cost play house. I did it with Fireboard from my work. After 15 minutes they would come out of a 4x6 playhouse sweaty in 50 degree weather.
The stuff sat out in the weather for almost 2 years and didn't mold or break down.
You might check around for companies in you area that dispose or recycle the stuff.
I plan on building a workshop in the future and this is probably what I will use for sound and heat insulation.
This is what I found in a one minute Google search http://www.flamerated.com/product.html go to the bottom of the page