Nikon AS15 adapter
AS-15
The connector in question is the Nikon AS-15 Brand Sync Terminal Adapter,Hot shoe to PC.
The camera hot shoe fires the flash, a Rohhs TT560, designed for Digital cameras including the Nikon D3000. I have heard the adapter described as a pass through circuit, which I assume to mean the hot shoe connector is wired directly to the PC Female connector on the side, in this case front, of the adapter which fits on the camera hot shoe. So I should be able to get a continuity reading with a volt ohm meter if the wiring is connected up internally. This is a long winded way of saying the unit is probably faulty and I should contact the seller and get a replacement.