If your disconnector is missing the catch, then you'd see the hammer following and the trigger would be "dead" as it would be after dry firing.
I don't believe JeffG's expectation of a slipping sear will be the case, but it's easy to test - pull the trigger and hold it hard to the rear, regain sight picture on target, and release the trigger. If the disconnector is catching but the sear slipping, when you release the trigger, it will fire again when you release the trigger to reset. Disconnector issues cause following (hammer chasing the bolt carrier into battery), slipping sears don't cause following if the shooter has proper trigger follow through, they cause doubles (the hammer will follow home then when the trigger is NOT held to the rear).
Most likely, as in 99% likelihood, it's a disconnector issue, simply not disconnector travel to catch the hammer with the trigger pulled.