Have you tried clearing your cache/cookies or using a different browser? 

when you get to the Setting page (in both Hangouts and in 1:1 Video Chat), do you see yourself in the video with right screen direction?  

Are you able to see yourself in Gmail video chat?
The best way to report an issue from hangout itself. 

Please verify your settings: Troubleshooting audio/video issues in Hangouts
Go through this troubleshooter: http://support.google.com/chat/bin/static.py?hl=en&ts=1712843&page=ts.cs