Bourne, I am curious, is your computer set to HYBRID Graphics mode, or Nvidia only? You can install the Nvidia Prime extension to find out if you haven't already.
Also, does your computer have a MUX switch? I ask, cause I remember once hitting that, and my computer didn't want to boot in the OS until I switch back. So I just use software to manage what GPU I am using.
I primarily stay in Nvidia graphics only. And a good way to test your GPU, is to set your computer to only use the Nvidia GPU. And if your computer fails to do that properly, that begins to point at the GPU.
I also second the idea of running MEMTEST. Good idea to check your RAM and make sure its ok, as RAM can go bad. And if things in the end point to your RAM. Turn off the computer, unplug the computer. Press the POWER button to discharge the caps.
Then remove the RAM, clean out the area with canned air, including the RAM chips, then re-install the RAM chips. Sometimes a good reseat fixes booting errors too. And you might want to do the same thing with the GPU, a good reseat.