Unfortunately, there is little you can do if you are facing some power related issue. I would recommend you to disconnect battery and power cable and hold the power button for 20 seconds. Reconnect the power cable and try to turn on the PC. Does the cooling fan start to spin? If there are no noises from the PC you may be facing a power port issue or a motherboard problem. I would recommend you to contact the technician. If the PC has warranty, contact the seller.
Hope this helps