You will achieve superior sound dampening by having greater density within your walls. If you are in a basement, the foundation is obviously thick enough -- but interior walls should be filled with gravel or similar material. There's a good description in the Sound Reinforcement Handbook. Carpeting, etc. dampens only a little. The egg crate foam works well for slicing up the reflectivity of the wall surface thus eliminating any latent room echo. Hospital bed pads (usually blue or beige) will work, but apply a layer or two of flat spray paint. You also need to look into the flammability of any material you attach to your walls -- don't want another Whitesnake event!

I have a thick blue carpet approx. 12x14 in good condition taken out of my daughter's bedroom. It's not quite as long as shag. If you want it, you can have it. It's clean. Just e-mail me. I have no truck to drop it off so you will need to come and get it.