I fixed the old monitor, and plugged it in - no problem. Started up, shut
down, started up again.

How did you fix the old monitor?

I have never come across a monitor having such a detrimental effect on
Windows - has anyone else come across this problem, and if so, any
suggestions?

I've never heard of this before. But I do have a suggestion, try booting
with the old monitor then uninstalling any monitor drivers. Plug in and boot
with the new one and see what happens. Maybe use safe mode.