Your hardware should be fine. To achieve the desired streaming capability, you need to increase your network bandwidth. Go to your ISP's website to see what options are available in your market (and at what cost). I suggest the "Extreme" package.
I'm planning on using OBS (Open Source Broadcasting) and I know Time Warner Cable is a peice of crap and I'm trying to convince my parents to switch but yeah I will definatley try switching to a higher package.