I´m having same problem right now with Asus HD 7850, bought in jan 2013. Week ago it started all of sudden. Kids were playing game, card just stopped working, vertical colour lines over all screen. Computer froze. After restart it worked OK, kids were playing game again for few minutes, then again, froze. This happened few times.
So I though I would re-install windows, it was about time to upgrade from 8.1. to 10. After install of new windows 10, it worked about one week. Without playing any games or even trying though. But then I downloaded Blizzard´s battlenet app, I tried to install SC 2 and during installation PC froze again. Same symptoms appeared but it got worse. Right now I can not log in, PC crash every time during login, it works in safe mode only - but screen is colour-noisy, when I try to install new drivers, card freezes every time.
I bought Arctic paste and applied it to the graphic chip, it did not help at all. I´m running PC on Intel HD graphic now.
I had new W10 installed, latest AMD drivers, right now I can do nothing, I guess card drop dead, cant try at other computer. I think it´s just too old.