I'm beginning to think it's must be a screen/cable issue. You said you've tried every possible cable combinations? What resolution are you running?
Edit: It may be an unresolvable problem when reading this thread: http://www.tomshardware.com/forum/364703-33-radeon-7850-screen-flickering
It seems to be a random problem for some people but apparantly it's not easy to pin point the problem. You could try to flash your BIOS to see if that helps (only do this if you know how).
Unfortunately I can't help you any further but make sure to return to this thread if you solve the problem and let us know.