U2711, DP, black screen, other issues

Really glad I saved this before posting, given that you can't create an account before your first post. Anyway...

I have three of these monitors, all of which I have bought recently (second hand obviously), but the most recent one is having some strange issues. The first thing I noticed was that when anything was plugged into DisplayPort, the connected device would act like it was connected and working fine, and the monitor knew it had a device connected (wouldn't go to sleep), but it just displayed a black screen (with backlight on). Even the actual monitor's menu wouldn't come up, and it would stay this way until I unplugged the cable, and then the monitor menu would work as normal. Until today when I have actually gotten the DisplayPort input to work, only it is a bit temperamental, and won't display at full resolution, only up to 1920x1080. If I change the resolution to 2560x1440 the screen just goes black, and then changing other settings makes the screen come back on, but at 1920x1080 again. So it was a relief to find that DisplayPort works in some way, but now I’d obviously like to get it working properly.

The other issue is that in general I can’t get it to display at full resolution properly with the other inputs. With a DisplayPort to DVI-D (dual Link) adapter and then DVI-D (dual Link) cable, I can only get 1650x1050 as the maximum resolution, although I’ve just tried that with one of my other monitors, with the same result. So could that be a limitation of the adapter? And the other thing I tried was just DVI-D all the way (using my work computer), and it displayed at full resolution, but everything looked very pixelated. That was using the same DVI-D cable, so could it be an issue with the cable?

I should also point out that this monitor was supposedly working fine (with the owner using DisplayPort at full resolution) before I bought it, but I wasn’t able to do enough testing on the spot to decide not to buy it. But it’s such a strange issue anyway – seems like it’s the firmware of the monitor itself, but I also wonder if a bump or something caused some damage, because it was transported just before I picked it up. But anyway, I’d appreciate any suggestions on what I could do to fix this, or anyone’s past experiences with similar issues. 

Windows 10 Pro 64-bit, HP EliteDesk G1 800 SFF, Intel Core i7-4790, 16GB Ram, AMD FirePro W4100 and Intel HD Graphics 4600 (I’ve tried plugging into both the motherboard and graphics card in trying to get this to work – graphics card only has 4 x Mini DisplayPort so all other tests have been on work computer and regular DisplayPort on motherboard of this computer)