You can test the electret by hooking it up as described in the previously posted schematic, these things take maybe 5 to 9 volts There is a FET intrinsic in the package. Hook up the mic to a oscilloscope if you have one, You should see a voice pattern.
Otherwise' plug it into your computer and make sure there is voltage to the mic coming from your computer. If it does not work with volts to the mike, and it is connected correctly, it is dead. This would be terrible, I think these things are maybe a buck. If no volts to mic, check your wires.
Usually the three pin ones are better than the two pin ones.
About the cap: These electrets have a pretty flat audio response from 20 Hz to 20 KHz, maybe someone wanted to filter out the higher freq to get a better voice response, as another person postulated. With only a few volts going to the mic it is unlikely the cap has failed. You can remove it though. Maybe there is a solder problem. You could check the cap with an ohmeter for a short just like it is now without removing it.
Wally