It is hard to find any info on that emachines desktop.
How many watts is the power supply (If you take take the side panel off, there should be a sticker on the power supply).
I don't think you could buy a GPU that can play BF3 on low unless you want to risk buying second-hand. Also most of the graphics cards that can handle bf3 will require a good power supply which will probably cost $50 or more.
I hope you didn't pay too much for that computer, you could save up and build your own which will be better than getting a customized hp.
I bought that computer one year ago for 399. and also the HP I'm going to get is a laptop so I can't really build it. I'm willing to up to one hundred dollars for both a video card and a new power supply if I have to.