Yeah, by the time you got all the necessary components that wouldn't bottleneck a 2gb card you might as well have a new system all together. Most people will tell you that you don't need an i7 processor (top of the line), but many will say that you should shoot for an i5.
For graphics cards you are looking for something that can play games at high-ultra settings at 1080p. Playing games at medium settings usually isn't much better than consoles. And as Nuke said, getting a card with 2gb Vram doesn't always mean you can play the latest games at good settings. All Vram does is increase the amount of texture memory available to you, which allows for much higher resolution textures, but only certain games get close to 2gb of vram and none that I'm aware of exceed 2gb without a texture mod. I'd say for graphics cards you are going to need at least a GTX 550 or AMD equivalent to get the type of performance that you want.
Then you needs a decent amount of ram, at least 4gb, but most people will say go with 8gb. Then a PSU of at least 500w, but probably more like 650-700w to be safe. Can't skimp on the PSU and get a really cheap one either.
Then, as others have said, you have to make sure your motherboard and case can accommodate all these parts, which they probably can't. So, at the end of the day you should just buy a new PC all together. If you build it yourself you can get a killer PC for under 1k, if not you can get the same PC prebuilt for about 1300. $1300 really isn't that much for a PC that will last you at least 3-4 years without any need to upgrade.
If I ever get another gaming PC I'm going to build my own, I'm too nervous about screwing it up to build it myself, so I would pay some type of third party to put it together and test it for me, costing about $200. Even with the extra 200 bucks it STILL would be wayy cheaper than most of the name brands like Alienware.