I'm assuming this is your first try mining with 3 cards in this particular system? Have you ever run the system with just one or two cards? I'm kind of wondering if the issue could be power related. Is your PSU a single rail 850W+ from a good manufacturer? Grab a program like GPU-Z (http://www.techpowerup.com/downloads/2244/techpowerup-gpu-z-v0-7-1/) and watch the +12V when you start up cgminer. If it drops down to something like 11.5V or fluctuates wildly in swings of .1V+ then you have some power issues. Normally a power supply would simply shut down if you try to pull too much current from it -- that's not happening in this case. Nonetheless, sometimes PSU manufacturers skimp to save on costs and leave out OCP (over current protection) which can then lead to the kind of symptoms you're experiencing.

It may turn out that your problem is not PSU related at all, but I figured I'd throw this out there since you've tried so many other things without solution.

Good luck