Thanks Jim!
After looking at your post I recalled that I ran across a preference file (the one in ~/Library/Preferences/ByHost/) that had a NoZBuffer flag.
I found the file again and sure enough it was set to true so you were right, no Z-buffer. I hand edited the flag to false and now my starfish is no longer a mutant!
Is there some way that I may have inadvertantly set that flag to true via a key command, preference setting or something?
Anyway, for anyone out there with similar problems, you may want to have them look at that setting.
And just to celebrate: I've attached a screenshot of my starfish right-side-out again.
-Ric