I mean that when you use the video output it is always good to check in System Settings -> Display to see if it is configured as you want it to be working.
Anyway, which video screen is black?
The YouTube's video frame or the whole screen?
On your display settings are you usin the external display as a second display or it is set up as a mirror of you Mac's screen?
Sometimes when you use it as an external display the windows are somewhere else hiding, and in your display settings there is a button to gather all windows so then you can arrange them as you please.