Interesting. When I read the title, I was pretty sure this was going to be an "I dropped the phone and now the screen is purple" post.
But since the screen is normal in Download mode, it sounds like it could be some bizarre software issue. I suspect the answer is "no," but just to be sure: Is your phone rooted, and have you installed a custom Kernel? (If you don't know what this means, then the answer is "no," unless you bought the phone used from someone else who did.
Anyway, probably not what you want to hear, but I think a factory reset is in order. A factory reset will, unfortunately, wipe your data stored on the internal memory, but I can't think of any other option if you can't use your screen. If your calendar, contacts and mail are synced with Google, you'll get those back after a reset, and the Play store will remember your apps and reload them, but not any app settings you may have customized. You could try downloading and installing Samsung's Kies app to your PC (Google search will find it), then connect your phone and see if you can back up anything else.
To factory reset: with the phone powered completely off, press and hold simultaneously the Volume UP, home and power keys. When you see the Samsung logo, immediately release all three buttons. You should see a text menu. Use the volume buttons to move up and down and select an option, then press the power button to execute that option.
You can try clearing cache first, but I don't think that will do anything. A Factory Reset might.