Desktop rebuilding will not help. It's a strictly Classic thing, which is why it can only be done in Classic.
My best guess is that you're copying your image file's icon, not the image itself. In OS X, you can choose to have image files show previews as their icons. However, these aren't their REAL icons. The real icon will be the generic gif/jpeg; the Finder will just load the image itself when it needs it and use that instead. A little confusing, I know.
So the thing to do is to open your image in Preview (or whatever image viewer you prefer), copy it, and then paste it onto your hard disk's icon. That should do it.
Hope this helps.