I am experiencing this same issue (Connect Failed: No Response) on a OBi508vs. It had been working great (4 GV lines) for almost the last year. The the last call I received on my actual phone was 3/8, and the last outbound call I was able to successfully place was 3/11. It hasn't worked since. Tried the usual troubleshooting (cycle power, check networking, check OBi connectivity...).
GV seems to work in the browser and on my cell phone app, but not on the 508.
I've read this entire thread now, and it doesn't seem there is much other news here except speculation about GV tightening security to eliminate unsupported devices and service terms abuse.
I'd love to know if there is an expected fix sometime soon.
-Patrick Ring