I just thought someone may have seen this type of problem before and knew what caused it.
Bunch of us here have, and its most likely that your video card has issues, when not a shared memory situation. The good thing is that for around $30+ USD you can get a healthy video card and put an end to this problem. But if you have the HD 5970 you will need to spend more to match that performance.
Would this video card happen to be covered by any warranty? Its an older card, but sometimes people buy older series cards on the cheap and it might be recent enough to be under warranty, however probably owned too long to be covered by warranty.
What is exact model of that video card. Looking online it might be this 5970 of the 5900 series from around 2010 when it came out...
https://www.newegg.com/Product/Product.aspx?Item=N82E16814102887 If so this was a costly video card when new.... did you get this second hand?
The damage with blocks that show and twinkle is usually the result of a cooked card, a video card that has been overheated. The GPU roasts and transistors with millions of them on the die, some of them fail from thermal failure and get into hung or unpredictable states making for the video card to wonk out the video or no video at all. You can also get lines. But usually blocks. Sometimes the system will boot and just some blocks but as the GPU heats up more and more blocks start to show. On video cards with damaged memory or systems with integrated video where some of the system RAM is shared with the GPU, a RAM problem can also act like a GPU issue, but its usually a refresh issue where stuff remains as ghosts on the desktop etc with memory issues, partial windows remaining that are not interactive etc.