Four hours is a LONG time for a budget laptop. There's this one:
http
/www.newegg.com/Product/Product.aspx?Item=N82E16834215406 but since it uses Intel HD (Highly Deficient) graphics, it may not be good for games.
If you go a little higher, and/or play the rebate game and win, this HP might do it for you:
http
/www.newegg.com/Product/Product.aspx?Item=N82E16834158218 . The graphics is a little better, and the battery life appears to be quite good. Expect it to be a gross exaggeration though, probably from a rundown test where the machine is sitting idle, not doing anything.