That clicking on startup is most likely the speaker relay engaging and cutting power to the speakers. Usually there are two ways that relay is powered: through the standby circuit and the thermal overload protection circuit. My guess is there is a fault in the protection circuit. When the amp is powered off, the voltage holding the relay is off, releasing the relay and when you power up, the fault causes the voltage to appear at the coil and engaging the relay which cuts out the speakers.
Try changing to each standby mode, powering down completely after each change. If nothing changes then that's probably what's at fault.