Actually I feel that your 700W PSU is fairly oversized. Although without knowing the concrete brand and type as well as technical specifications it's hard to say. I've had some no-name/cheap PSU with > 500W in my lab which was unable to deliver more than 200W on 12V; on the other hand I've had many 300W well-known brand (Silverstone, Seasonic,...) PSU which were perfectly able to power even much more demanding hardware fairly above 300W in total.
It happens to me as well once that a graphics card won't work when connected to two PCIe 6-Pin connectors if they are connected to the same rail. The solution was to use one PCIe 6-Pin connector from the PSU and use an adapter from 6-Pin PCIe to 2xMolex 4-Pin which was included in the graphics card bundle.
In general you're right with your calculation:
96W max power consumption at 12V it's a maximum of 8A current. However this is split on several sources. PCIe cards are rated as follows:
- PCIe board connector: Max. 75W
- PCIe 6-Pin connector: Max. 75W
- PCIe 8-Pin connector: Max. 150W
So for example a card with just one 6-Pin connector is allowed to take a maximum of 150W (75W from the board connector and 75W from 6-Pin PCIe power connector).
A card with 2x 8-Pin connector is allowed to take a maximum of 375W.
Even a card with two PCIe 6-Pin connectors (max. 225W) should work with a power supply rated 700W.
Remember that most modern power supplies deliver quite low power on 5V rails so all power is usually delivered via 12V connectors.
You should probably check all your power connections. Modern borads usually use the following connectors:
- ATX 24-Pin power connector (make sure not to use a 20-Pin connector)
- EATX12V 8-Pin connector (sometimes just a 4-Pin 12V connector on the mainboard, often referred as the "P4-connector".
The EATX12V connector is basically there to power the CPU. Some mainboards might refuse to start if you connect it to a PSU using a 20-Pin ATX connector instead of 24-Pin.
So in your case I recommend to try some PCIe 6-Pin adapters and hooking up the graphics card to two Molex 4-Pin connectors from different cable rails (yes, you should use two different cables, not connecting both Molex-connectors to the same cable). If you don't have such a power adapter you can get one cheap from your trusted hardware vendor.
I personally really cannot imagine that your 700W PSU cannot power your setup. Here I am running an nVidita 8800GTS-512, Intel Q6600@3.1GHz, Maximus Formula, 4x 1TB HDD, TV-Card, PhysX P100 card and Asus Xonar soundcard on a Silverstone ST50+ PSU (500W).