With almost every type of ATX or other modern motherboard, the PSU must present a 'power good' signal
to the motherboard sensor before it (the motherboard) will show active signs. This 'power good' signal is a +5 volt level, or very close to that. Too low, and the sensor will not give the clearance to the motherboard circuits to become active. Could be several reasons this signal is either too low or not present.. faulty PSU, excessive power load, or faulty motherboard component (possibly capacitor?). That 'power good' lead is the gray wire at the rear of the main power plug. Use only a digital multi-meter to check the voltage.. an analog type will load the circuit too heavily. The signal is presented within a second or two, after the PSU has stabilized its load to the system.
It is not advised to do so except by a professional, but use a 47-ohm 1 watt resistor to bridge from a +5 volt (red) lead to that gray wire.. and note if the voltage comes to about +5volts. The motherboard should show activity then. But do not keep this bridge in place too long, as there may be a circuit problem elsewhere and the motherboard can be fatally damaged.
F@H.. to solve mankind's maladies.. in our lifetimes!