If you have any parts you can salvage from old machines (cases, hard drives, monitor, key board, etc...) and you are willing to play games at low to medium quality, you may be able to build a AMD APU type machine. I did this with a AMD 7850K, with water cooling, which allows me to overclock the graphics significantly. I reused an old case, and old HD, RAM, etc, and came in around your budget. I never meant this to be a long term gaming machine though, just something to get me by until the next generation hardware comes out.