The motherboard doesn't have a price. If you already have the mobo then that build is better than this one. Though mine with a mobo does come within your budget. On-die GPU though so gaming will be less that spectacular. I'm sure someone will come along with a better build than mine.
http://uk.pcpartpicker.com/p/OEKN
Edit: oops forgot to include storage...
Modified version of your build:
http://uk.pcpartpicker.com/p/OERY