I'm having this problem too when using Skyrim and League of Legends. I'm not having any problem running old games like Mechwarrior 4 or surfing the internet and watching youtube. But whenever I switch to a newer game, within the first 5 minutes there'll be a crash. Guaranteed.
IDK if it means we have different problems, but i've never gotten the teal/brown pattern. I get either greyscale vertical lines or full black, only once did i have red/brown vertical lines.
I've tried contacting AMD with a bug report, but they have yet to respond.
EDIT: Taking out the card and running on the integrated graphics I can play Skyrim and LoL no problem.