I have exactly the same problem with my charger (regular, weak flashing light and no charge going to the Surface (the 12V cable from the black box), even though the USB charging (5V cable from the black box works fine).
I did all of the above fixes and nothing worked.
I have a second power cable which all works fine.
I suggest it's a problem somewhere either in the box that supplies the 12V or in the cable that leads to the surface, but that's probably no help to John. Maybe the MS people will read this though?