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How about switching to the kernel of the AMD APP matrix multiplication sample?
It's 0K. I fixed it. Although, I don't know how I did it. I've tampered with project settings, borrowed some code from AMD's samples, and rewritten some of my code. Somewhere along the line, everything started working just fine. I wish I knew what made the difference so I wouldn't repeat the same mistake again, but right now I'm happy just to see it work - I lost more than a week trying to figure out what's wrong and was at the end of my wits' when I posted the question.
Thank's for the quick responses.