I'm having the same issue. Installed Yosemite, installed all available software updates through the App Store, and iTunes still won't open. If I dig into the app contents and run the actual executable it opens, but that doesn't help me when I want to launch from Spotlight or the Dock.
Drag the iTunes icon in your dock onto the desktop so that it disappears. Go to the Applications folder and highlight the iTunes icon (left click once) and drag it to your dock. Then try opening it by double clicking the icon in the dock.
It's possible that the old icon (short cut) is to the previous version of iTunes which no longer exists so it does nothing.;D
I have found this occurs sometimes when a totally new version of an app is installed.