Ipad not charging, or switching on

Help! Ipad 3 will not power up, nor charge. I've tried different connectors, charging from the mains and through the USB on a computer.

I have also put it into recovery mode and restored to factory settings through Itunes. This seems to work ok, right up to the point where the Ipad should reboot. It switches off, but doesn't restart.

Is it likely to be a hardware problem? Should I try and change the dock connector, or am I missing something simple.