I had a situation with my computer to dac that sounds similar (not very loud though) and found the culprit to be the rca cable running parallel to my power cord. As soon as I separated the cables the click stopped.
Wadia iTransport problem
I've just received my iTransport yesterday and got it connected. When I put it on the digital output mode with a DAC. There is a "click-Clack, click-clack" sound every time when I pressed the "STOP" or the "FORWARD NEXT" button. The noise level is quite high. I'm afraid it might demage the speakers. I also tried it on another DAC with another amplifier system. Same thing happened. Anyone have this problem ?