While it's not a sure thing I'd pull the GPU card out (always be safe with the ESD and don't use swiffers.)
Now gently run the erase over the contacts (this is on the web.) Then replace the GPU heatsink compound.
You didn't reveal if this is in or out of warranty. While I cringe at the thought of a swiffer, you may try the warranty angle. But the symptoms are on track with a bad GPU.
So yesterday I decided to clean my computer especially the cpu fan, as it got pretty loud under load which didn't happen when there wasn't as much dust in it.
I touched grounded metal (heater) and the case before doing anything but stupidly, so freaking stupidly, I used a dust cleaner, like a swiffer, and swiped over the back of the pcb. I'm quite sure this is where there must have been an esd (did not notice at that point). It might have been when I accidentally slightly touched the pcie connector.
Later that evening, I played some CS:GO. Up until the second game there were zero problems until my pc crashed with a striped screen and wouldn't start again correctly (grey/black screen and nothing happens). Today, I did a clean Windows 8.1 install, which I had to because I couldn't update to it because my user folders were moved...
Now it starts up and doesn't crash as long as I use the "Microsoft Basic Display Adapter" driver but there are graphical glitches all over the place (horizontal green bars in wide vertical bars).
If I install the proper driver (AMD Catalyst Beta/ Non-beta or through windows update) nothing works anymore like when all this started.
Now, I have to use the integrated HD4000... Can I do anything here or is the graphics card irreparably destroyed? It is a 2.5 years old Sapphire HD 7870.
I appreciate any help/comments.