A sure-fire way to tell whether too-low 12V start current is the problem is to hook up a known working, older, generic 300W PSU to the afflicted system. If max power was the problem, it would have a hard time starting, or not start at all. But invariably, with these too-low 12V start current situations, such PSUs (even several years old ones that long precede 24-pin ATX outputs, etc.) will start the system fine.