Yes, this is a very common problem. The speaker itself is fine. The problem is caused by leaking capacitors on the circuit board. The goop is conductive, and causes things to be connected that shouldn't be. Symptoms include squawks, groans, burps, chirps and...silence.

You'll have to open it up and clean all the goop off. For a permanent fix, you'll also need to replace all of the capacitors. Some lazy folks (like me) have gotten away with just the clean (in a dishwasher, no less!), but that's just a short-term hack.