I bought and installed a new 2560-1440-display. I am sure of the resolution and double checked it.
I first connected it to my video card (Palit GeForce 770 GTX, 2*DVI, HDMI output) through the HDMI cable.
The result was that the only resolution that worked was 1920x1080 in the windows-screen resolution.
I switched from HDMI to DVI-D connection (also see here) and the result was that suddenly, the screen's true resolution of 1440p was shown in the display settings, but when set, the screen was still blurry. Taking a picture or a program and pulling to another screen made it appear perfectly. I used the nVidida Control Center to choose a custom resolution at 24, 30 or 37 Hz (instead of the 60 Hz that it is set to automatically), following this problem: here. Choosing this did the trick in this way: It showed the message "do you want to keep this resolution?" for a few seconds. During this message, the screen was crystal clear, like I want it. I clicked yes, and it switched to just as blurry as before.
(I then updated my graphics driver, with the result that the DVI-Adapter did not work anymore. At one point, the computer would boot and show the BIOS information on the new screen, but this would claim "no signal" when Windows was booted up. I now got this to work again though, only to face the problem from the paragraph above.)
Despite updated drivers and DVI-D connection, and the video card being able to handle 1440p according to here, what else can I do?