My iPad won't play iTunes when my PC is shut down?

If you are using the sharing library part of iTunes with the ipad which I use then there is a good reason. If you are using that, then it connects to the pc when iTunes is up and going in the background. Where if you turn the pc off iTunes closes with it. Therefore you can not connect because the pc is giving the music over the wifi and if the computer is not on no music over wifi unless you use something like pandora

If you are playing music from the computer to your iPad using Home Sharing your computer must be on.

http://i1224.photobucket.com/albums/ee374/Diavonex/2a6ea8913d7f123c0b1ea6a29fd30 221_zpsf9845974.jpg

You have to sync Music to iPad

http://ipad.about.com/od/iPad_Guide/ss/How-To-Sync-An-iPad-With-iTunes-Music-Mov ies-Apps_3.htm