Loose laptop screen: how to tighten it?

I've got this old relic, an Apple PowerBook, and I'm running into a bit of an issue. When I lift the screen, it stays in whatever position I set, but there’s a lot of "play" or looseness in the hinge. It wasn't doing this before.
I have no idea how to tighten the hinges. I just can't get to them. I tried popping off the plastic bezel around the display, but all I found were two screws holding the panel to the casing, so that didn't help at all.
From the outside, the hinges are covered by a chrome trim piece, but I haven't been able to pry it off.
Anyone have any ideas?
Here's a photo of what I'm looking at

You need to pop those chrome covers off. They're just clipped on, so you'll have to give them a little nudge to get them loose.