Foam inside a case helps damp out case vibration and resonance, but because the case can't be sealed it won't reduce fan and drive noise much, if at all.
The route to quiet PCs is large fans operating on reduced voltages, big cpu coolers, quiet or ideally fanless graphics cards, psu built to keep noise down etc.
The PC in my sig has two Noctua 140mm fans, one at the back as an extractor, one on a big Noctua cpu cooler. Graphics and psu are fanless. With the fans running at 7 volts it puts out around 26-28dB at one metre. With the fans running on 5 volts it's so quiet my decibel metre can't measure it.
www.silentpcreview.com is a very useful site for all sorts of information about making PCs quiet. It can be done, but a case change alone won't achieve much.