Ah, I finally got the hidden files to show. Deleting the .db cache did not solve the problem, however. The globes remain. 'Favicons' will stay in IE8's favorites folder as they always have. However, I am thinking Microsoft removed the "Favicon on desktop" style that XP had, due to having to not being able to automatically have IE as default browser in Win 7. Nobody at Microsoft Tech Support can help, only advise that 'you can't count on it because "they listened to user feedback!"' Sorry, I don't understand, unless the free source advocates have won some kind of concession from MS.
Notice: on a clean install of Win 7, that IE8 is NOT on the desktop! You have to drag & drop it from the start menu to the desktop to get it out there. Even so, it's just one of the list in Startup Menu, and one has to "Pin" it to have it show at the top of the menu. There's been some code changes, folks, and I'm not happy. I'll bet using another browser as 'default browser' won't let you save shortcuts to the desktop as Windows indicates it will, with the 'favicon's' present.