Battery Indicator Button Not Working

It is clear that just the button itself is malfunctioning.

I would spray it with contact spray or dab it with 90%+ IPA and see if it works, just in case it was due to grime.

If not, it needs replacing but some of those button assemblies are welded - not sure about your model - and once they are removed, can't be glued back in place.

So you need to be very careful when replacing it (if doable) and not pry anything off or screw too tight.

EDIT/UPDATE:

@henchr

Since I looked at the new picture I can tell you your problem right away: the button / micro-switch itself is missing.

Underneath the silver button there should be a rubber gasket. Underneath that gasket a button attached to the circle showing in your picture. Where's that button?

I guess it's broken off, and like you have to replace the battery indicator flat cable assembly. Like @alinorne (Kevin) said, it shouldn't be expensive to come by and a pretty easy fix.

Second, what I mean by fragile: the plate is screwed onto the side of the computer through 3 screws that go into 3 screw brackets. Those screw brackets are welded onto the the side frame. If they break off (don't over tighten your screws!!!!), they're a pain to put back - if feasible. I have yet to find a satisfying way to glue them back. If someone can share a good way I'll be thankful.