Laptop display not recognized - Dual boot elementary and Windows 10

Question

So I recently bought a laptop :

i7-6700HQ
16Go DDR4
Nvidia GeForce GTX 1070
SSD 250Go
HDD 2To

It came without any installed operating system and I would like to run both Win10 and Elementary OS.

What I have :
- Win10 installed on a 125Go partition (SSD)
- Bootable USB with latest Elementary OS release

What I want :
- Win10
- Elementary OS on the spare SSD's 125Go
- A mean to choose which system to boot

Experienced problem :
When booting on the live Elementary USB I either get :
- a completely black screen ;
- a blinking 'e' splash screen ;
- an underscore char and a black screen.

What I already tried :
- Using rufus software and messing around with its settings to create the bootable USB
- Editing the start command replacing 'quiet splash' with 'nomodeset'

I can't even get to run the live version... Elementary's logo keeps blinking over and over without going further... Doesn't my hardware have support for Elementary OS ? What am I missing ?

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UPDATE

I managed to install Elementary OS alongside Windows 10 by plugging-in an external display. However, my initial monitor (the laptop's one) still isn't recognized by eOS.

I tried installing Nvidia additional drivers as in https://elementaryforums.com/index.php?threads/howto-install-nvidia-amd-driver-in-elementaryos-the-official-way.206/
Still no luck...
Any help on how to properly detect my laptop display would be greatly appreciated.

---

UPDATE 2

The laptop's monitor is working at splash screen ('e' logo showing) but nothing else happens unless I plug an external HDMI display.

Answer 1

Your graphics card should be perfectly supported. I also have a 1070 in my desktop PC and assuming your information is correct you also have the desktop card in your notebook.

I dont know if this will work but try installing the newest NVIDIA driver like this in the terminal.

sudo apt-get purge nvidia*   # removes old driver and all the configs
sudo add-apt-repository ppa:graphics-drivers/ppa       # adds repository
sudo apt-get update    # to update the repository you just added
sudo apt-get dist-upgrade # when youre at it you might as well run this to ensure you run the latest OS version
sudo apt-get install nvidia-375 # to install the driver again as of right now 375 is the newest stable version you can look that up on the nvidia website