Problem with Samsung UN55B6000 54.6 in. HDTV LCD TV I have already replaced the power supply in the Samsung UN55B6000 and still have a clicking relay and no power when I plug in TV. What else could be wrong?

The Power supply unit being replaced as it had failed in the first case can be due to continuous high drain current of the components. This is similar to a short and can make the power supply fluctuate and oscillate as the error of high current is detected.
Now disconnection of the power line to the invertor or the main board must stop the SHUNTING and you will be able to ISOLATE the suspected circuit.
Care must be taken to check the path of the drain which will lead you to the suspected component. As a tip check for the component that is heating up and this can assist you to confirm the case. Attempt only if you are equipped and do not take chances on the board.

Hello
Just check its backlight inverter board for any shorted components in it. Then check further. This is a common fault to most of the Samsung LCDs which I've faced. The symptome will be the same as you say. Disconnect the supply line to backlight inverter and see whether there is any click sound heard. If not, make sure that backlight inverter board is faulty, and slhould be replaced with same type and number. If there is stll click sound, main board is fauty. OK.