Upgrade PC for streaming 1080 60fps

Hi, I have been wanting to upgrade my PC from the junk it is to be able to stream games on a good video setting. The games I play are LoL, Diablo 3 but will be picking up the new Dragon Age and GTA. Would I be able to upgrade my PC to do this or should I just build a new one. Any suggestions on upgrades/parts would be great. Thanks!

Current PC:
Motherboard: Asus M5A97 LE R2.0
PSU: LEPA N500 500w
CPU: AMD FX(tm)-4130 Quad-Core Processor 3.8GHz
GPU: NVIDIA GeForce 9800 GT
4GB of RAM

Looking mainly for upgrade parts to last for a few months before upgrading again, or a new PC for around 1000-1500 if building a new PC is a better choice.

9800 GT is holding it back.
new GPU, more ram, SSD if you don't have one, CPU is fine. new PSU if you need one.
I'd get an 8gb stick now then just have 8's in your next build.
wait for Fiji for gpu

If you only get stuff you can carry over to a future build then nothing is lost.

I would upgrade the processor if you have the cache as well. Streaming will take some extra processing power. I'd recommend getting something like an FX-6300 at least.

indeed but GPU and Ram first.

What is your motherboard?, Is it a good clocker, will it take a much nicer CPU?

If you are going to throw your CPU away you may as well burn it to death first ;)

http://pcpartpicker.com/p/hWf2NG An I7 and 980 alternative if you want to do a new rig entirely. The I7 and 980 combo is going to stream much better then the 6300 or 8350 can, while maintaining better fps minimums and averages. This I7 in particular being a 6 core really should excel at streaming, since you should have 2 completely unused cores in most games.

My motherboard isnt that great. It is Asus M5A97 LE R2.0 and power supply is LEPA N500 500w