EDIT: No system will boot without RAM installed. Just an FYI
Other than the above. It's bad hardware. Question is, where?
Honestly, the problem could be a lot of things ranging from the AC adapter, a surface mount component on the MB, to a microscopic crack in one of the ball grid array connectors that mates a CPU/CPU to the surface of the motherboard itself. Sometimes you can reflow it (handled by the manufacture or via professional services) with heat to correct the problem. But at the end of the day, yeah, a HW problem