Did the dock ever work?
If not, I would take the dock to a nearby store that has the TF300T on display. See if the dock works with another tablet.
If not, the dock is bad and should be returned/exchanged/repaired.
If the dock works with the other tablet, there is an issue with your tablet and it should be returned/exchanged/repaired.
The battery charging circuit is completely separate from the keyboard and USB functionality, so USB/SD slot and charging can work and the keyboard may not.