I've had this problem twice now with a brand new Phantom 2 Vision (all updates applied).  Charge up the battery, plug it in, run through the start up procedure, TX on, extender on, cam on WiFi, push the battery button once, then again and hold - just one blink from all the LEDS and nothing.

I took the top off and reset all the connectors, no change.  Then I unplugged the camera connector and plugged it back in, and the quad started normally.
Do I have an issue with the quad, the camera module, or something else? One blink of LEDs is not in any of the manuals.
Scott

I have found that as the camera moves the cable can sometimes pull, this usually causes no telemetry and no video on the app, as you say I have had to pull cable out (with no power on) and pull the cable out of the camera and then firmly push it back in again.

Try moving your cable so as to lessen the pull or movement when the camera moves.