I am having the exact same issue. I can run 3 cards full bore no problem, add in the 4th card and it gets nothing but hardware errors or I have to lower the intensity from 18 to 13 and remove any overclocking on it, while the other 3 maintain overclock and 18 intensity just fine.
Here is the setup.
ASRock 970 Extreme 4 Current Bios v2.60
8GB DDR3 1600mhz RAM (2x4)
AMD Sempron 145 stock no OC/Core Unlock (tried and it didnt happen easily so didnt bother)
(4) 6950 PowerColor 2GB
Running AMD Catalyst 13.11 Beta9.5 (forget off top of head but its the most current Beta Drivers posted as of yesterday)
PSU is (1) 850W for 3 cards and (1) 600W for the 4th card (Even tried on the one 850W since it has 8 PCIe 8pin power connectors but split power to rule out it as the problem).
As far as connection goes, I have 3 of them solid on 16x non powered risers in the 16x slots. They each get 485khash per card. When I add the 4th card via a 1x to 16x Powered Riser (tried both with and without power connector) same results if I get into Windows and am able to fire up CGMiner, with all 4 on same CGMiner the card will get HWs and very low hashrates like double digit low or start at 200s and drop down to eventually get called SICK.
And if I tried to just run the 1x card by itself in a solo CGMiner session it gets the same results (no other cards running). I'm just so frustrated on what to do as I have a card that is basically sitting useless.
I also tried to rule out the Riser as the problem and plugged it into a 16x slot and it worked fine. So that tells me its not the video card (as I changed them around as well) and the riser is working. I checked the BIOS there is nothing in bios in relation to the PCIE slots other than the voltage setting and spread spectrum.
Really at my whits end with trying to make this work when everyone/where else I see posted with practically the exact same spec albeit 7950s for video cards working just fine. HELP please