That's not a good thing. Or at least may not be. Have you checked to see if it got turned off in the BIOS? Also, even without the light, your OS may still be aware of it. Try that lspci command and check for anything that looks like wireless or 'broadcom'.
I once had a friend who couldn't get the integrated wireless in his laptop to work. Knowing how these things go from experience, I started from the bottom and asked him to confirm that his laptop actually had integrated wireless. It didn't.