Did you find a solution ?
I have the same issues with AMD 6770M & HD 3000 Graphics, since 1 week, all day I make tests with no solution..
First of all I tested a large number of drivers without success, I also tested several operating systems, win10, w7, ubuntu, again w7 etc.
Then I came across a post on the AMD forum where someone explained that this was a symptom of a faulty graphic chipset (https://community.amd.com/t5/drivers-software/black-screen-after-installing-ati-drivers-hp-laptop-sw...). The “solution” was therefore to “re-flow”, to heat the chipset to a temperature above 230 ° C for a few minutes.
However, it is not very stable and I may run into issues on games during my testing.
I'll see if limiting the frame rate will prevent blues screens.
To be continued..