Buying a laptop - recommendations?

So i just found out that the laptop I've had in repairs (under warranty) for 7 weeks (no league for nearly 2 months, gah) isn't going to be fixed and is being bought out.

My last unit was an i5 core for around $800 CDN before taxes and warranty (was also a touchscreen, which i don't need). I started playing league AFTER buying the laptop, and noticed it wasn't quite good enough - i played on the lowest graphics settings to avoid issues, medium seemed to cause lag. The issue may also have been Internet, I've moved so that should be rectified.

Anyways, to the point, I'm looking to buy a laptop. League is the only game i play, so i don't need it to be able to run other games. I DO need a laptop that can also be used for general purposes (studying, work, etc...).

What I'm looking for: Runs league without any problems! Probably an i7 core Decent battery life - longer is better, but minimum 4 hours moderate screen size: ideally 13.5'' to 15.8''. Good brightness / viewing angles so i can see everything nice keyboard - i type a lot outside of league at least 2 usb ports Centered fan or other good cooling process - i hate when the fan runs hard while the computer is really cool near it and really hot on the far side.

Extra bonuses : A number pad would be great HDMI port other relevant ports? note anything else you like about the laptop

Budget: I can be flexible, but I'd definitely like to look for something under $1500 CDN ($1350 CDN before tax). If i can get away with under $1000 ($850 before tax) that'd be amazing.

Please let me know if what you're using seems to fit what I'm looking for. I'm particularly interested in hearing about units that you've played league on without problems like lag at at least medium graphic settings (or just not minimum). Please include a price or guess at the price if you can!

Cheers!