It can't be done. Not with the Monitor included at least. It would have to be a AMD based system unless you want a i3 and you might want to use Linux Mint or Ubuntu as your Operating System.
1920x1080 Monitor - $100
i5 - $200
GPU- $150
That leaves about $200 for your hard drive, your case, your power supply, and Windows. Psh, I forgot the motherboard. Yup it can't be done unless you want a bad low end computer with yester-years technology.