Welcome to the forums. This particular problem has been quite a common occurrence lately. If your Corolla has a dimmer switch for the instrument cluster (located on the dash to the left of the steering wheel) then it is most likely the rheostat that has blown. You can pick one up at a junkyard very cheaply.
All you have to do is pop the plastic piece out that houses the air vent by pulling it gently with a flathead screwdriver from the bottom (there's a small rectangular cut-out in the plastic for this exact purpose). It will simply pop out if you pull it towards you. You'll then be able to unplug the connector and remove the dimmer switch/rheostat. From memory, the switch comes out from the back once you release the clips holding it in place, so don't try pushing it out of the hole.
Good luck!