I would imagine 850W is enough for a two GPU set-up... if you have a spare 500W+ laying around, hook one of the cards up to it, and use a paper-clip to turn the PSU on without it being plugged into the mobo [pictured below]... if that fixes the problem then it might be a PSU issue.
Sounds exactly like my issue when I was trying to run my cards on a 630W Antec PSU. I know the 7950s require more power than my cards, but I was pretty sure someone told me they were running 3 7950s on an 850W...
Do you have a lot of other drives plugged in? CD/DVD/multiple HDD?
