OK, I officially hate my Mac mini.
I have tried every suggestion in this thread, and I have tried everything in the KBs linked in this thread, and I conclude that my Mac Mini is a POS that was made in China at 4:30 PM on a Friday.
I have absolutely zero sound from my monitor with sound set to output via HDMI to it. It used to work just fine.
I have absolutely zero sound through internal speakers EXCEPT alert sounds. This also used to work.
No sound from iTunes, no sound from the web. And now I can't insert a disc into my external CD ROM. And I when I try to access my CD ROM to see if there's a disk inside to eject, the only options I get are what to do if I insert a disc (e.g. launch itunes if it's a music CD, etc.).
So I just shut down my Mac Mini (again), and the Samsung monitor, and then powered them back up. Then I had no sounds at all, except for itunes and alert sounds -- through the internal speaker. I went into settings and checked the sounds, and for some reason, the restart changed my output settings from the Samsung HDMI device to internal speaker. When I select the HDMI output, itunes will play itunes radio through my monitor's speakers! Hooray! Problem solved, right? Uh uh.
Still no web audio - at all.
Still can't insert a disc in the CD ROM.
I have another Mac Mini that is also connected via HDMI to a TV / Monitor, and have never had to configure anything, and it has just worked. ***, Apple?
Have I mentioned that I hate my Mac Mini?
For all the reputation that Apple has had with making elegant, user-intuitive devices, I have to say the company absolutely ***** in this regard in the past couple of years. Quality control and consistency and user intuitiveness have gone swirling down the Foxcon toilet. I have two identical iPads that I bought the same day. The iOS load is identical, but one has features in the settings that are only supposed to exist on the 3G models, and the other doesn't. I took it in to the Genius Bar, and the guy said "wow, that's weird. It's not supposed to have that." I have other iPads that I configure for people at work, and have run into several instances where identical models with the same iOS but the options in settings are different (i.e. some settings don't even appear in one, but exist in another).
I guess there's something to be said for Steve Jobs' petulant nano-management that kept Apple in line.
I still hate my Mac Mini.