Please do try these troubleshooting steps that I've suggested to others who had the same problem.
- Do a hard reset, remove the battery and AC adapter then press and hold the power button for 20 seconds then see if it will boot up normally.
- Next is to test the AC adapter and see if it's supplying enough voltage to power the laptop or better yet try another AC adapter that has the same voltage.
- If there are lights on the laptop indicating it's on, connect an external monitor again and see if you'll get a display. If there will be a display on the external display that means its the built in display that has the problem but try to press the Windows key + P at the same time and select Display Only.
- Also do try and reseat the RAM, remove them all for couple of seconds then put them back in making sure that they are all seated properly into each slot.
- If all these will not work I would contact HP for a repair or replacement since it's just a month old laptop.