the solution: an AMD APU build.

$500 (well, just over, but if $15 breaks the budget you really shouldn't be looking at a PC) with OS:
case: http://www.newegg.com/Product/Product.aspx?Item=N82E16811147122
PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817151077
motherboard: http://www.newegg.com/Product/Product.aspx?Item=N82E16813157465
APU: http://www.newegg.com/Product/Product.aspx?Item=N82E16819113360
RAM: http://www.newegg.com/Product/Product.aspx?Item=N82E16820231546
HDD: http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769
OS: http://www.newegg.com/Product/Product.aspx?Item=N82E16832116986