Most all of the battery DOAs I've heard of won't light up the LED's to report full charge. Usually NO LEDs will light up and the battery won't take a charge. Your battery sounds like an exception. It sounds more like a connector problem. Have you inspected the connector and compared it to the other batteries to insure the contacts are "intact". It seems unlikely the connector is damaged, but it's unusual the battery made a connection to get charged 100%, yet it cannot make connection to the drone to start up. Definitely sounds like a defective battery if the other two batteries work OK.
This isn't common what you're describing, but in general DOA batteries have been reported, not uncommon. You should return the battery to where you bought it and see if they'll swap it out.