The screen on my laptop (Samsung NP350VC) is broken and I use it only through an external monitor. After changing from UEFI to Legacy Boot I can no longer access the BIOS through the external monitor (it won't output over HDMI or VGA until past this stage). Is there a method by which I can access this and re-enable UEFI?
Open the laptop and try flushing BIOS back to defaults by removing the battery and/or setting the respective jumper.
Otherwise, unless you have memorized order of the menus and can go through them blindly, the wise choice might be to take the laptop to a repair shop and have them connect it to a similar screen temporarily, to fix the issue.