Thank you.

I already ordered a 7870 two days ago
Yes, I monitored my GPU temperatures, everything green (55°C @ 99% usage)

The card is working again (I wrote the post above by using onboard vga).

It seems, that its the mainboard or CPU which was damaged...
I get the first pictures on the monitor after I logged into Windows. (also no UEFI screen with onboard or grafic card so i dont think its a OS/Software issue)
I already checked the RAM, next will be CPU with prime.

Any furhter ideas?