850w is more than plenty for two 7930s (essentially what they are).
In comparison I had two 7870 hawks [for a while] with a 600w psu and I was fine. Make sure both cards are running normally by themselves before paying out for a decent PSU. I had a look over the specs of your psu and it should be fine with xfire/sli with a single 12v rail. Have you overclocked your PC? If so try stock, again to make sure.
Sounds dumb, but hey, make sure you've connected the right cables to everything, for the cpu, mb, gpu's. It could be the cards trying to draw more power from the m/b than what the m/b can supply.
If none of the above does anything, get yourself a nice Seasonic/corsair/Coolermaster based PSU. Myself I use coolermaster branded PSU's; nearly a decade of use and no faults/problems so something must be working