Laptop under 800 dollars?

My lenovo y510p failes on me and i voided the warranty by modding the cooling. I then realized i don't need so much power in a laptop. Id like your opinions on the best laptop between 13 and 15 inches, with a dual core i5, integrated hd 4400- hd4600 graphics, and preferably full HD (i'm fine with HD too, as long as the screen is on the smaller side 11-14 inch).