back in the early Genesis 1000-5000 and before, Weber had a very cryptic and much less informative system of marking their grills. Even if you find the sticker and a "serial number", it may not tell you any real specifics about the grill. And that if you can even read it any more.
But, I would look between the control panel and extra burner on the side of the control panel. Then under the control panel and maybe even the extra burner. Another place to check is on the manifold.