|More questions I'm afraid:|
When you are playing the video (with the black screen), does the time bar move along and do you get any sound?
I think we've about eliminated Flash player but go here from each browser and see if it reports that you are now using version 11-2-202-235 (in the square box):
You should also be able to get to the same place by right clicking the black screen and choosing "About Flash Player..."
It doesn't seem to be a browser issue. Seems odd that YouTube plays OK. Am still thinking about it and have a few other ideas after you've checked out the above.
EDIT. Try these:
Disable any advert or pop-up blockers.
Right click a video, select Settings and disable or enable hardware acceleration from far left icon.
Always pop back and let us know the outcome - thanks