Google Hangouts Stuck and Unable to Sign in
Solved it!
Go into Privacy in Google Chrome's settings. Clear your browser data. It looks like it had cached the wrong authentication key for me.
Sometimes you need to reset Synced Data
https://www.google.com/settings/chrome/sync
click Reset Sync Data at the bottom.
Note: You will lose synced data, unless that data is currently on your computer(you didn't clear history)