YouTube uses Flash, so it is most likely your Adobe Flash Player that is causing the trouble. It's grabbed the computer's sound system and hasn't let it go once you've finished playing the video.

Nothing to do with MIDI or NWC specially; any other program that wants to make a noise would fail too.

Apart from Joe's suggestion, you might be able to kill off a Flash Player process to release the sound system for other programs to use, but when I tried just now it wasn't obvious how to do that. I assume you tried closing your web browser before playing MIDIs etc?

Anahata