I've seen this before - when I mixed cables from different brands of PSU's.  The click is the give-away, it's preventing starting up due to a short.

I'd plug one card direct into the pci-e 16x slot, and try a PSU/cable combo that's known to go together.

(I tried mixing EVGA cables with a Rosewill PSU, same result, connectors are the same, pinouts at the PSU end are different).