What GPU are you trying to install? 

This is what the seller told me:

Hi, sorry you’re having troubles. I’ve sold more than a dozen of these and no one has reported this issue. After some reading it seems your card may not have a compatibility boot mode. You may want to try a different card to get around this, perhaps a friend or another old system? One other thought is, even though you’d be doing it blind, you could try to boot into safe mode by pressing f8 or f11 at boot. Then using the arrow keys me enter to select safe mode. Perhaps then it would allow output from your card and you could install drivers that work. I don’t have the original graphics card in my possession so that is not an option.

One other option I could think of, is unplug the internal hard drive and boot from a usb stick or other hard drive you have with a copy of windows or maybe even Linux and modify from there. Also, maybe try resetting the bios by removing the battery for a minute or so?

It's a PNY GTX 1060.

Stick the 1060 in a working PC, use the Nvidia firmware update tool (per PNY, also works with their GeForce GPUs), update vBIOS on the 1060. Then stick the 1060 back in the Alienware R10 and see if it solves the problem. 

https://www.nvidia.com/content/DriverDownload-March2009/confirmation.php?url=/Windows/uefi/firmware/1.0/NVIDIA_DisplayPort_Firmware_Updater_1.0-x64.exe&firmware=1&lang=us&type=Other

Note, with the update, the 1060 should work without needing to disable secureboot. 

Note, the link is for a 64 bit OS.  

I don't understand the question. You don't have to turn the computer on at all until the card is installed. Meantime you have integrated graphics to connect the monitor to check if the computer works. See the manual

 Alienware Aurora Ryzen Edition Setup and Specifications (dell.com)

Service manual- Alienware Aurora Ryzen Edition Service Manual | Dell US

The vBIOS update should resolve the issue though.

R10 doesn't have integrated graphics support on motherboard.  Not an option.