I've tried rebooting, tried detecting via both Catalyst Control Center (the ATI software) and the default Windows 7 display options. Theres nothing wrong with the monitor, as it works on other computers.
The monitor I'm trying to get working is a VGA, but the DP is DVI-D, so I also bought a DVI-D>VGA adapter.
So the connection looks like this:
[DisplayPort > DVI-D] - [DVI-D > VGA] - [VGA > Monitor]
Kind of a mess, but I see no reason why it shouldn't work, those are just adapters. It would have been safer to buy a DVI cable, but none of my monitors accept DVI, only VGA.
I'm 100% certain that the monitor is fine, the DisplayPort is compatible with VGA (says so on the box) and my card can take 3 monitors, as it's designed for EYEfinity.