My PC is very silent, almost unhearable. I got some cheap engine soundinsulation mats, which are made of a kind of foam with aluminium foil on one side and sticky stuff on the other. I put that all over the inside of my case leaving as few holes as possible (otherwise sound will escape through the holes) and it worked very well.
The only thing to watch out for is that the mats are heat insulating so you need to make sure that you have good airflow through the case or your cpu and other things will overheat. You need at least one case fan. I bought a near silent Pabst one.
In my case cooling was actually improved since all the air is now sucked in through the front of the case where I left a hole in the sound insulation, which causes all the air to travel from the front, over the cpu, and out the back. Before I put in the sound insulation there were holes all over the place in the case where air was sucked in.