By "disappeared off the left corner of the screen", I was referring to the windows minimize animation.
I think I know what happened:
Somehow, when I clicked the zoom button to switch to the mini-player, it drew the mini-player almost off-screen in the lower left-hand corner. Looking carefully, I could see a quarter-inch sticking out. I couldn't grab it, because that was a hot-corner for my screensaver. I turned off the hot-corner, then I was able to grab it, and presto, back in business.
Thanks for the tip about "Username/Library/Preferences/com.apple.iTune". It probably would have worked by resetting the location of the mini-player to the default. I probably would have had some extra work opening my library, which is on another disk, etc...