Wow that doesn't look so good, sorry though as I'm not sure what the problem is. BF2 runs fine on my 4000+ san diego/7800GTX. Have you checked temps and such? Updated all drivers? Could even just be problems with BF2 and not your computer because a lot of people seem to have problems with it...
At first when I looked at it it seemed like a complete piece of crap, and I thought for sure that Nintendo was doomed on this one, but then as I read more and more about it and thought about it, I started to like it. Needless to say the design is growing on me for some reason. I won't make any...
I also have 2GB. I have played it on a friends computer with only 1gb and it lags for the first couple minutes of gameplay. Big difference really, I'm also usually the first in game.