Not mentioned, but if there are mobo monitor connections, try those, too.
But yes, this is almost definitely a hardware problem since it's also happening in Windows. The only other plausible option would be the hardware's firmware, but that seems unlikely...
It could theoretically be an incredible fluke to have a software issue in both Windows and Linux... Maybe the same weird edge-case hardware interaction that's the same between two versions of a closed-source NVidia driver? I can't see that as plausible, though.
If OP is in a developed country, used monitors are cheap. My vertically-oriented side monitor I got for $20, and I only even paid that much because I needed one that could go vertical orientation without a monitor arm.