The Chromebook ninjas solved it. I emailed them describing my issue, they responded within a few hours and said to "verify [my] Microphone and Webcam setting by going into Gmail settings then clicking on the chat tab. Under Voice and video chat you can verify settings." once I did that it magically started working! I didn't have to change any settings, just verify them. They really are ninjas!
Now that I think about it, do you think they changed (or could change) my settings to fix it since, after all, it is all in the cloud. This thought is both awesome and really scary.