Parts for a cheap gaming PC?

I'm new to this whole thing but I really want to build my next PC. I need to save as much money as possible and if possible, reuse some of my old parts if I can. By the way, I'm not a hardcore gamer, as in I don't want to run the best quality games at ultra settings with 60 fps+. I just want to run games like League of Legends (high settings at all times and be able to stream and make videos without lag at any point in the game), Runescape on high, Assassins Creed: Black Flag on med-high with atleast 40 fps, Battlefield on high, Skyrim on med- high, minecraft on high. Those are pretty much games I want to be able to play at good fps rates.

Specs:

Operating system: Windows 7 Home Premium 64-bit
MOBO: Gigabyte H55M-S2H
Processor: Intel(R) Core(TM) i3 CPU 540 @ 3.07GHz (4 CPUs), ~3.1GHz
Memory: 4096MB RAM (not sure about the brand, probably not gaming-quality ram)
Display: AMD Radeon HD 5670
PSU: Corsair 560HX
Case: I don't know how to find what case I'm using, but I know it isn't a gaming case.
HDD: Seagate 500 gig
Monitor: not sure but its an Asus and the highest resolution is 1400x900

I'm most worried about a new graphics card, mobo, and cpu. I want to know if I can reuse the other parts. If you guys can find me a build hopefully under 500 dollars and considering any reusable parts and the fact that I want to save as MUCH money as possible cause of my parents and ****. Lol.

Decide on a definitive budget, precise, then come back and ask when you have it.
The computer trade now is switching and moving so fast, what someone may recommend now, in 3 months time when you have the money say! May then recommend something else, as new technology is coming out so fast.
You could look spend a 100 on a gpu that is out now, and in 3 months when you have the money, there will be a better one for the same money.
Wait a little bit, Intel got 20 new cpu's out this year, and some amd hardware is looking for drops in prices as well.
PS for what you want to do,500 won't get it,1000 and you be about there.