The z-buffer is also called the depth buffer and is one of the parameters in the PixelFormat class you passed to Display.create().
PixelFormat(int bpp, int alpha, int depth, int stencil, int samples
depth should be 16 or 24
From the way you are talking, though, it sounds like you are already doing this :lol:
The code I think we want to look at is the code that renders the object (and possibly the code that sets up the rendering state).
Another idea: Is it possible to post a screenshot (or maybe a short avi of the problem)?