Notebook Video, Display and Touch

So basically i bought this laptop 4 months ago, a lot of problems with it.

This blue screen issue started when i was playing FXIV and the pc randomly died and bluescreened with the video error.

After restarting the Nvidia 3060 Laptop GPU was nowhere to be seen since it got disconected.

After another boot it comes back, this error happens constantly and depending on the game requirements it takes more or less time, from games like FFXIV to Roblox.

One more thing the notebook as horrible battery life standing at maximum of 2:30 Hours while just browsing the web, which is sad since I need it for work and university.
I've tried everything, from reinstalling the drivers on different version, running hp hardware check, checking event logs and absolutely nothing seems to work or fix it so at this point i suspect is just a GPU or Motherboard issue.

Its a "new" laptop and already running like this which is sad and really unacceptable.

The laptop is new, no damage done to it and still acts like this.

The performance and temps run good with the exception of the GPU reaching slightly high temperatures, but nothing alarming for a GPU standards.

I really need help cause the laptop is on warranty, I know a fair amount about laptops and this is not normal at all.

I can't lose or stay without this laptop since I urgently need it for work and for university.