Hmm, conflicting requirements, 'cause "high powered" fights "portable/long battery life" and "gaming/high def screen" fights 13". Are you POSITIVE you must have all this in a mobile package? You could get a lot more bang for your buck if you mainly game in your dorm room (or wherever). For $1500 you could easily get
- a pretty beefy desktop gaming system/workstation with a 24" hi-res monitor and full sized keyboard and mouse
- a slim netbook or converting tablet that would be easy to carry and take notes on, and even run light/medium games and apps. 9-10" or so means you can slip it in a vest or coat pocket, 13" means lugging a bag which makes it easier to forget, and more likely to be left behind when you don't think you'll need it but later you find you do.
I personally do it this way, the laptop to do all I want was crazy expensive, and I'm already mortified every time I drop/bump my netbook, which happens fairly frequently :p Having 2 means kind of a pain keeping em sync'd, but if you set it up right you're also backing up your stuff as you go, which is a HUGE plus for me ('cause otherwise I almost never get to it). You're way more "future proof" too, because it's easy and WAY cheaper to upgrade the desktop system. And "desktop" doesn't have to mean a monster - if you really want some portability, you can fit it in a slim case that could fit in a backpack, even with the monitor and keyboard.
Even if you decide "must all be in laptop" I really recommend getting the desktop monitor and keyboard, and docking it when you're at home - the difference in keyboards and screen real estate is HUGE. And you can still get a small tablet or big smartphone.