The worst problem here is that people are quoting $400 desktops missing important things like screens. You cannot compare a "headless" build to a laptop. You must include a screen to even begin to compare.
For the OP... the laptop you will be looking at in the $400 range will not be a gaming laptop. It will be an economy laptop with an APU that can game to some degree.
As long as you understand that your budget severely limits you in this case, and that even $50 desktop GPUs or lower-end APUs will be outperforming the laptop in question, it IS possible.
As of now, I cannot find anything quickly under $400 that isn't a netbook-level cpu/gpu. The closest I found was a Gateway with an A6/7520G for $443.
http
/www.newegg.com/Product/Product.aspx?Item=N82E16834215950
It is theoretically possible to find a deal or refurb to drop it below $400, so keep your eyes open, but even then the A6 isn't going to set any land speed records.
The others I found below $400 have netbook-level processors and GPUs.
http
/www.newegg.com/Product/Product.aspx?Item=N82E16834310622
That's a Lenovo G-series with an E1-1200 and 7310. (not really recommended for gaming)
A refurb or friend selling an old laptop might be doable, but those are risky business. Even if the seller is honest and gently used his laptop, an older laptop is closer to the end of its useful life. Furthurmore, you are more than likely going to be disappointed with gaming on such hardware.