Hi smutek,
From your experiments it really looks a hardware problem. You can try to swap cables around but it's likely the device. It's pretty bad news really.
I don't know if you have options for a replacement, it depends on the manufacturer.
If you need to get a new device I can point you to
http://www.displaylink.com/shop/index.php
You may want to get a USB 3 device: the new chip generation has better compression even over USB2.
Cheers,
Carlo