I like to watch sports with no sound, with the stereo playing music. I really do not like to listen to the constant chatter of the sports announcers. I only un-mute to hear what the flag (in football) was for, sometimes.
As for not realizing music was playing, I have the opposite problem: Sometimes when napping, or waking up, I can hear music playing (in my head I guess) and it sounds like I just left the stereo on. Usually the music is one of my favorites.
Another oddity of mine is upon hearing a sudden, unexpected noise, I see a burst of fireworks, or kaleidoscope like lightshow, every time it is different, but encompasses my entire visual field for a split second.
The sound must be unexpected for it to happen, and it actually does not have to be very loud, and it never lasts more than a very short time, well under a second.
