Can I stream?

Hello, Sythe.

My most recent laptop didn't have 3D acceleration, so there was absolutely no possible way to stream.

I'm assuming there's no possible way now without dropping too many frames, but I would like to know whether or not it's because my specs, download/upload speeds, or both preventing me from being able to stream on this laptop. There's a laptop I'm going to buy next (this is a relatives I'm using for now) that should be able to stream pretty well. I didn't even expect this laptop to be able to stream at all, so I was fairly surprised that it was able to even though it was dropping frames left n' right.

Anyway, here are the specs of my current laptop:

Processor: AMD A6-1450 APU with Radeon(TM) HD Graphics
1.00 GHz
Installed memory (RAM): 4.00 GB (3.44 GB usable)
System type: 64-bit Operating System, x64-based processor

Download Speed: 10.46 Mbps
Upload Speed: 3.41 Mbps

1.) With those details, is there any possible way to stream 'Old School RuneScape' without dropping frames?

2.) If not, what's preventing me from doing so? Is it due to my low computer specs, upload/download speeds, or both?

3.) I have a budget of about $1,000-$1,250. Which one would you go with? (please back up your choice with a reason) I'm looking for a 'fast' laptop that can stream and one I can conduct business on. (eg. buying/selling RuneScape, WoW, LoL, ES, & Diablo currency) Also, I'd even like to possibly start learning to play League of Legends. Here are my options: here

Speaking of LoL, is my current laptop with the above specs sufficient enough to run League of Legends without lag?

Thanks for your replies in advance.