When I use the /playsound command, I add a mob. bit. It goes kind of like this when I type in playsound: 'playsound mob.ghast.scream' (that's when I want a ghast scream).
You cannot use a specific noise, as I have tried that, and it does not work, for example 'mob.ghast.scream1'. You have to take away the number. Unfortunately, that means that you will not be able to have a specific zombie moan, so then there will be a random moan of a zombie every time you activate the command block. This is how I would type in a perfect playsound command: 'playsound mob.zombie.moan @p (or username)'.
I also check that the command block's redstone is wired up correctly by typing in the command '/say @a hello'. If the redstone works correctly, it would say to everyone on the server (or just you if it's on single player) 'hello'. This ensures that the command block works when the redstone turns on. If you're still stuck, I'm terribly, terribly sorry but I will no longer be able to help you, as this is most of my knowledge put into a forum post.