since that you can boot into safe mode I have to ask you:
does your system post boot (right when you power on and display the boot info or the logo) without the external monitor? or nothing shows up?
if it does show anything before it goes to black this indicates that it's a soft issue, otherwise it it related either to your display card or the mainbord.
if you boot with nothing showing on screen please follow this:
- remove the ram modules.
- remove the mainboard battery.
- remove the battery.
- wait for a minute or so.
- put everything back.
- press and hold the start button for 15 seconds (reset).
OK, let's start troubleshooting with a clean OS
the very first thing we need to do is to boot into safe mode and when windows load it self into safe mode go to power off choose restart while pressing shift key.
this will force the machine to restart into recovery mode.
of course doing all that require you to use the external monitor.
after you've recovered your windows into a clean state and still having the black screen then we can treat it as a hardware issue.
I don't know if you do have the tools to get on going troubleshooting the hardware but I will assume that you do.
so first of all you will connect your original screen to another working machine to check if it is working or not.
if it is working step two is to remove the display adapter and test it on another machine if that goes to nothing too
I suppose that the only thing left for us is the mainbord.
one more advice
since this is a fairly new machine try using the nearest support center.
and get the use of the warranty.