BSOD with atikmdag.sys error with brand new GPU

I have a problem with my new GPU. Few months ago I've bought Gigabyte Radeon R9 270x 2GB OC and installed it in my computer. Then I've noticed strange black squares appearing randomly in my browser [Mozilla Firefox] while I'm on websites like tumblr or Facebok. I sent GPU back for repair but they said everything was fine.
Then I got 2 BSODs. Both displaying atikmdag.sys as error. They both happened while I was playing League of Legends though I'm not sure it has anything to do with it.
I've tried numerous versions of GPU drivers but none helped. I still get those black squares while browsing. They dont appear in video games or while I work in programmes like 3ds max.
I've attached a picture of those squares and a DM Log I've done. If someone knows how to fix this I will be very grateful.
Thanks.

ninetears said:

I've tried numerous versions of GPU drivers but none helped.

There are two crash dumps included in the zip. One is of 18/10/14 and the other is of 15/01/15. Both of them happened with 14.4 WHQL installed only.

So we cannot be sure that it is the behavior there irrespective of the driver version installed. Try Download AMD Catalyst 14.9 WHQL Driver ... see how it goes. Let us see any BSOD with this driver installed (not suggesting you to get the latest 14.12, intentionally).

Stress test the Graphics Card using Furmark.

Video Card - Stress Test with Furmark

Take a screenshot of the furmark window before closing it. Upload the screenshot for us.

Also, make it sure that the hardware acceleration is turned off in Firefox. Firefox GPU Hardware Acceleration - Turn On or Off

Let us know the results.