Itunes doesn't authorize the computer or sign in

I am not able to authorize the computer when I sync my both phones iphone 6 & 5 with latest ios.

Infact Account -> Sign In or Account-> Authorizations -> Authorise this computer menus in Itunes don't have any effect. Nothing happens when i select them in menu. No popup, no username/password window.

Anything related to the Account also doesnot work in itunes store.

For Example "Account" link under Quick links in Itunes Store page doesnot work.

I tried to reinstall itunes by deleting it from applications and reinstalling from dmg. No effect.

I cleaned all the apps from the itunes.