Will The Load Causes No Power Symptom?
Yes definitely, if there is any shorted component in the load/motherboard the power supply will not start. Non polar cap, transistors, diode, ICs can become shorted to ground in one of the output power line and this will cause a zero output voltage in the power supply. Sometimes you could hear a noise in the power supply but usually it will be quiet.
If you have checked that all the primary side components and the secondary output diodes are good then focus your search on the load. Try remove one output line and power on (you need to isolate the problem after the secondary diode). If there is a slight changes in voltage (assuming the zero volt suddenly increase to few volts) then you may conclude that the line could have a shorted or leaky component.
If removing one line does not have any changes in the voltage then try on another line. If the load consist of less components, a normal analogue meter that set to x 1 ohm could be used to detect the short circuit. If the load consist of high density of component like a large mother board that have hundreds of small non polar cap and ICs then you may need a short circuit finder tester to locate it.