mixlex, welcome to the forums.
There may or may not be any screws holding it on, will have to look carefully from the inside to see if there are. If there aren't any (and good chance even if there are) that there will be two or three tabs like this,
top and bottom (and possibly in the middle), down both sides that can be popped out with a gentle push. If fact I found this review of that model, Gateway DX4300 Review
and if you scroll down there is a picture of the inside towrards the front and you can just see one of those tabs,