Sounds like driver issues. Had the same problem when I first started with my 5850.
Had to do a fresh install of Windows and used Catalyst 13.1 and everything worked fine.
I'm using 13.4 at the moment. Can I downgrade it without reinstalling Windows?
You might be able to. I needed a fresh install because I was using an NVIDIA card before putting in my 5850, then I proceeded to download like 5 different versions of Catalyst and SDK so I couldn't get it to work right. I finally got cgminer to work but then was getting nonce errors.
Uninstall everything and use Catalyst 13.1 and see if it works.
The errors definitely look like driver errors though.
Once you get GUIminer working, I suggest moving to cgminer. You will notice better hashrates with that.