I've had similar issues, I solved it by rebooting the phone and plugging it in using sony usb charger until the charge is over 30%, after I got mine to 30% using usb, it then was able to charge using the dock.
you could check the dock with a multimeter, but there's not really much to the dock itself, so unless it's a broken wire, the problem is with the wall charger which the docks plugged into or the phone
main phone: Sony Xperia Z1
+ Sony Xperia Z (given to wife but i still tweak it, much to her dismay)
Previous Android phones (RIP):Samsung Galaxy( notes 1 & 2, S2 & S3), Nexus S and original Galaxy; Sony Arc and X10
Who said crapple invented the smartphone??? before Android I used windows mobile and symbian devices for years!