PSU Amperage Question

Hi, I'm in the process of building my second computer, and I've run into a PSU question for which I wasn't prepared. I was originally going to do an AMD A8 build for my wife, so I picked up an Antec Earthwatts 380 for it when I saw it go on sale at Newegg. However, one of my colleagues was recently kind enough to offer me her old GeForce 7900 GS for the build. That's roughly the same graphics horsepower according to the Tom's Hierarchy, and frees me up to spend a little more of my budget on a processor. (My wife's needs are fairly minimal...light gaming, some HD television streaming, but I want to get her a reasonably good CPU to future-proof it. I can upgrade the GPU whenever it becomes necessary.)

The problem is that the card specifically requires a 400W+ PSU and 20A on the 12V rail. Mine is 20W short on that, and the 12V1 rail is only 17A (the 12V2 rail is 15A). I checked the box and the 12V rails can, together, supply 336W. The 7900 GS, as I understand it, draws 82W.

Do you think I can get away with using this card? The rest of the computer will have a couple of RAM sticks, maybe 4 fans total, a DVD-RW player, an SSD, some decent motherboard in the $60-80 range, and either an Ivy Bridge i3 or an FX-6300. The only parts I haven't purchased yet are the processor, mobo, and GPU.