The 1st GPU VRM are toast or dying. Run cgminer with -d 1 -c conf.conf
if it runs, then the second gpu is fine. You can try dropping the voltage/clocks to the first gpu or keeping it disabled and only using 1/2 the card.
I think you are right! if I run cgminner -d 1 the second GPU works perfectly.
If I try cgminer -d 0 I have to add -I 10, then it works very slowly, but only for 5 or 10 seconds, then got that error again (regardless of which clock settings)
Any chances to fix the 5970 or is the first GPU-chip itself the Problem?