Could be a bad motherboard, most issues like yours are caused by that. Did you try different RAM? Go over system to make sure there are no heat issues, check fans, vents, re-do headsink with new thermal paste. Another thing to try is to remove the battery and also the CMOS battery if system has one, then hold in the power button for about 30 seconds. Plug it in wall power only and see if it turns on. If it does, replace the batteries and try again.