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?
Umh, just to mention, you could get two 7950ies. These are much cooler than the 7870ies.