The mobo had onboard graphics so I can confirm that both the screen and the rest of the setup works fine.
Now I've given them my old Sparkle nVidia 9800GT (passively cooled) and when I boot up (even on the BIOS screen, ruling out any Windows driver issues) everything on-screen looks like it's been smeared across the screen and is all blurry, and at times it'll move the whole display off-centre so half the display is off-screen.
The monitor is VGA, so I'm using a VGA-DVI adapter, which I've confirmed works by using an old PC with DVI Graphics card.
The card works in my own computer, ruling out any worries I had of me damaging the card in transit to my parent's house.
It also previously worked on their monitor in my PC when I lived there.
So from this it seems that:
-The card itself is fine.
-The monitor is fine.
-The adapter is fine.
-All cables and connections are fine.
-The graphics card does work on the monitor.
So I'm guessing that means that this must be some weird compatibility issue with the rest of the system, but that also seems unlikely as my own system is running a higher end ASUS Mobo, the same RAM but 4GB and an i5 2500k, plus a 600w PSU.
And I can't run any further tests on the system and monitor until I next visit my family in a week or two unfortunately.