Sorry mate but that's the truth, your system is dated by 5 years now and quite a bit behind the times for playing the latest games. That gts 250 is basically a rebadged 9800 gtx, which really is even an older gpu. And no, there is no way for you to get your system working at 1080p res even on low settings at a decent frame rate. I'm surprised you can even get 20fps.
If you want to play PC games, time to pay to play. New system if you really want to get the true BF3 experience and honestly, it won't cost you as much as you think.
I built this PC in May of 2009 and I'm in college now so all my money goes towards that. I will probably have this computer for at least 3 more years.
I am aware that the parts are fairly old, but it does decent enough. I can get ~50 fps on Skyrim on medium settings, and ~45 on Starcraft II on high settings, so I was expecting a bit better out of low on this game. I know Battlefield 3 is suppose to be the 1000 pound gorilla for graphics, but that doesn't mean that low settings should still tax your system THAT much.