Can you enter BIOS? If you can, check if the hardware components are properly recognized. It seems to me that this is not a power issue. I would say it is more likely to be RAM memory related. If your laptop has some warranty left, I recommend you to contact the reseller. Some hardware changes may be required.
If you do not have warranty left, use the laptop's manual and check if the CMOS battery could be easily reached. It it is, remove it for a few seconds, put it back and try starting up the laptop.