Buying a New computer, need help(Has to be a Laptop..Explained in post)

So I'll start this off with, ONE..i don't know crap about computers. TWO..unfortunately, the new computer HAS to be a laptop(desktop would be useless to me..as i cant carry it around with my busy life. I'm rarely at home, and if I am, its to sleep). With the recent updated to SR I am forced to invest in a new laptop, my current laptop is somewhere around 4 years old. I have played League on it since just after season 1 ended. During that time I have enjoyed playing the game, but always have had it on low graphics due to it bogging the system down. I may have only played at 20-25 fps the whole time, but I loved it for what it was.

With the update(yes, I did test it multiple times With bots, didn't dare try with players) my computer runs the new rift at 5-15 fps once everything gets going(minions spawn etc.) So..begrudgingly and with a hard choice to make I am buying a new computer. I have a set price range that i can spend on it, and even then its still hard to pull off. I can spend up to 800$ with an easy down payment of 400$ if payment options are available for the laptop. I am looking for a laptop, that can run League, Skype and have a browser up in the background all at the same time and still run league at 60fps with no lag. BUT, the main deal, is having league at 60fps. So, any input will help greatly, I just want to be able to play league again without the problems of the graphics bogging it down.