Really nice computer here: http
/www.amazon.com/HP-15-p030nr-15-6-Inch-Special-Ed...
Sadly, it is $9 above your budget. It has
AMD A8-5545M 1.7 GHz 4 core CPU,
8 GB DDR3L SDRAM,
1 TB 5400 rpm Hard Drive, 15.6-Inch Screen,
AMD Radeon HD 8510G graphics,
Windows 8.1
The other problem is, it is kind of laggy if you run DayZ at full settings.
EDIT:
This laptop is $25 over budget but is a great deal: http
/www.amazon.com/Acer-Aspire-V3-572G-54S6-Gaming-Laptop/dp/B00MM2WA8O/
This laptop should be able to play DayZ at full settings at a decent frame rate.
EDIT TO THE EDIT: It is cheaper here:
http/www.newegg.com/Product/Product.aspx?Item=N82E16834314535