Have you checked your voltages on the PCIexpress-Supply connectors? How much Watts can your Power Supply deliver? Which manufacturer made your Power Supply?
What you describe sounds like the Power Supply is unable to deliver enough juice to the card and once it has to do something the voltages drop too low to distinguish between 1 and 0 on the signal-lines.
Once you're sure the PSU is not the problem, you can start looking at the Graphics-Card itself. If you have an Oscilloscope, you can check for ripple-voltage on supply-rails of the card itself and if they look okay, then you are probably dealing with a faulty chip or a cracked solder joint on the Graphics Card.
Also, if possible, check if the cards work in another PC. If they do and you eliminated the PSU as the cause of the fault, you are likely to look at a problem on the Mainboard.