I'm have a very similar issue with my Surface Pro 3 and Plugable UGA-4KDP DisplayPort Adapter.
Everything was working fine (I've had this adapter for 4-6 weeks) until this morning - the screen goes active but is black (monitor is active, not in power save mode).
If I go to Screen Resolution the monitor is correctly identified, and is active (set to Extend displays, not disconnected).
Windows thinks the monitor is there because I can move my mouse and drag windows into the extended area (I just can't see anything).
I've completely uninstalled the DisplayLink software (using the cleaner tool), and restarted/reinstalled - but no go, same issue.
Seems like similar issues at the bottom of this thread:
http://displaylink.org/forum/showthread.php?p=75879