I got my new dock - and I had the same problem. I took all the parts and swapped them round with someone's set up and here's what happened.
My power cords work with my usual Surface Pro power supply unit
My Surface Pro charges on the other power cord/power supply/dock
My new dock works (well charges the Surface Pro) when I use the other power cord/power supply/dock
Therefore it seems the failed unit is the power supply that came with my first dock. When I got the new dock it did not come with a new power supply unit.
Can Microsoft replace this? If it turns out both the old and new docks work I will gladly return the new dock.