How to troubleshoot "iPhoto unable to connect to Photo Stream"?
Solution 1:
System Preferences -> iCloud, Check Photo Stream.
Solution 2:
FWIW I fixed mine when I realised I'd probably downloaded iPhoto using an AppleID from the App Store but logged into iCloud with a different AppleID. I deleted iPhoto and it's related files (but not the iPhoto Library) using CleanApp, entered the App Store with my usual AppleID and downloaded iPhoto again. Once the App Store, the downloaded iPhoto and iCloud logins were the same iPhoto Stream worked again.