The core problem appears to be that I cannot log into my iTunes account, at least from one computer. I'm running iTunes 12.3.2 on Mavericks, both fully updated. I discovered the problem trying to update apps. I went to the "My Apps" tab and tried to download one (of serveral) apps needing updating. Up pops the window asking for my iTunes password, which I duly entered. No download, and about 2sec later up pops the window again. No statement about the Apple ID or password being bad, just a second request for the password. This is a never-ending loop of download failure followed by password request. Tried it on several apps needing update with the same result. Tried going to the App Store - blank page. I then tried to check my iTunes account info, same result. Went online and changed my password, same result as in trying to update an app. Logged out of iCloud and back in, same result. Interestingly, I tried syncing with my iPhone which has all apps updated, and the sync process didn't transfer over any of the apps needing updating. However, if I try logging in to my iTunes account via iTunes on my laptop, all is OK.