At $40 the only option is the AMD HD 6450. It can play most games at lower settings. It will run LoL on low-med settings with aa off.
To give a bit of an example an intel g31 with the GMA graphics would get a 3dmark06 score of around 300. The same motherboard and cpu will get a 3dmark 06 score of around 6,000. Thats a huge improvment. Another good thing about the 6450 is it comes in low pro and it only uses about 20 watts of electricity so it will work in any computer with any PSU.http://www.newegg.com/Product/Product.aspx?Item=N82E16814125431