Anyway the GRUB thing was a red herring, looks like you need nomodeset — do you have full graphical support with that parameter applied?
Not quite!
With the BIOS set to "Intel Linux", Debian boots, but I have no display or keyboard (for any OS). If I do boot Debian, case I can use nomodeset to "see" my login screen now that it boots, and it seems fully functional (how to verify?).
With the BIOS set to "Windows", Debian doesn't even get to GRUB. The screen doesn't even get past the BIOS ""Press Del to enter" screen. But at least I can see that frozen screen on the laptop itself
.
I need to be able to boot Debian in "Windows" mode, just like Ubuntu can. I presume I can do this with a different bootloader. The Ubuntu one didn't work, but now I'm thinking that since I have access to Debian (albeit via an external screen), I can use that to replace GRUB with something else (rEFInd probably).
EDIT:
Changing the bootloader worked. rEFInd will boot Debian under "windows" mode, and so I can use Debian with the laptop's screen, keyboard and mouse. Further I no longer need nomodeset to fix display problems.
rEFInd presents two Linux options, which I presume were autodetected:
1) Boot vmlinuz-4.9.0-7-amd64 from 244 MiB ex2 volume
2) Boot EFI\debian\grubx64.efi from system partition
As expected, 1) works and 2) does not.