You can test this with a multimeter. Put the meter in continuity mode on the bare speaker, and see what it does. If it comes up as .0L or beeps, the speaker is dead shorted and has to be replaced. If it reads some low voltage like .001 the speaker is either not making contact, or it has blown without a dead short.

You can use this teardown as a reference to remove the speaker to test. Cleaning may help too, but don't hold your breath.