You won't find a gaming laptop for that budget, but you could certainly get a desktop for that price that will do some games. This would actually be byogamingpc's forte.
If you don't have the technical skill to build your own desktop, my suggestion would be to find a built desktop with no video card, that has either 4 GB or 8 GB of RAM, and an i5 CPU (preferably i5, but you can get away with an i3). Then just buy a cheap but decent video card and install it. It won't run modern games on full graphical settings is all.