I want a cheap gaming laptop

Hello,
My budget is $600-799
I would like it to be under 15" however over 17" is out of the question
I would like a 3rd gen i7 core processor and also a good graphics card so i can play games like
Call of Duty, Minecraft, Skyrim, High quality games
Brand name anything but gateway,lenovo, toshiba
and also I would like a 1-4 hrs or more battery i dont have that much money so if there's a 400$ one that has an i5 processor instead i just want a good laptop to replace my
acer 5251
PLZ reply and help me