Here is a build that will beast most games incredibly well (Will Minecraft about 300-500fps), and decently do the extremly intesive games (about 100fps or more.) As for the portable monitor and the battery back, you gotta find that yourself. The build: http://pcpartpicker.com/p/VtbHD3
You need to give your Minecraft account away! Forgetting something that important! I even cooked Notch a cake on Minecraft and you just forget! Mind you, that cake was good.
