My macbook pro won't go to sleep when I close the lid

I've been having this problem for a couple of years now, and it's getting pretty annoying.

I got this MacBook Pro in April of 2011. Otherwise, it works great. It goes to sleep when I go up to the apple menu and select "sleep." BUT, when I close the lid, it stays on. Heaven forbid I don't have it plugged in, because then the battery will be shot! It also won't go to sleep automatically when I leave it for a long time. Yet another potential battery drain.

How do I fix it so that it goes to sleep automatically when I close the lid and when I leave it alone for a while?

In Energy Saver, I have checked all the boxes necessary: "Put the hard disk(s) to sleep when possible" "Wake for network access" and "Automatically reduce brightness before display goes to sleep."

Am I missing something here, or does my computer just have a defect?