Hard to say where to begin on that kind of budget.
My first instinct would be to find the best graphics card you can afford right now like this one....http://www.newegg.com/Product/Product.aspx?Item=N82E16814127616
However, it won't run at full speed since your slot is PCI-e x 16 and the card is 2.0 x 16 and many benchmarks are run using at least a previous generation i5 to achieve 1080p.
I think you really need a new mobo/CPU/RAM/GPU solution and that's going to run closer to 300-400.
You could go with an AMD APU/board combo (CPU with graphics) but the latest ones use DDR3 so you'd have to buy a combo AND new RAM.
I'm hoping someone else adds more to this thread but as far as I'm concerned the first way to boost gaming power is through the GPU, but only works if the rest of your system can work with it.