lol. Dude, a $650 PC will likely perform less than your current computer. Case in point: http://www.newegg.com/Product/Product.aspx?Item=N82E16883229284
. Has a 2500K, which is ZOMG epic, but the GPU is crap and performs less than your 5770 does. Plus, its $680, which is a snag outside of what you wanted. Add in the cost of a new GPU, it isn't worth it man.
Besides, your CPU is a capable gamer. Upgrading to the 2500K would only result in about a 7 FPS increase in most games. You'll see a hell of a lot more bang for buck just upgrading the GPU alone. Save the rest of the money and put that towards a better computer when Ivy comes out. Or Haswell in 2013.
What is your PSU? How many watts does it have? Gotta know this to suggest a good GPU.
Also, are you running 64-bit windows? Gotta have that to really make use of the RAM you got. RAM is super cheap, you can add more RAM for $20 if necessary.