You may have to replace the dock in the device as for videos it uses the mic next to the camera for default apps and when using 3rd party apps it will use the mic in the dock. Test the voice recorder app on the phone and if it shows no change in pitch will need a new dock.
When a mobile phone is blacklisted, only the IMEI is meaning all the parts around the motherboard are still good for use. Just keep in mind the motherboard is the phone so prices will be pretty high just for a board but to answer the question, once changed will work fine.
There is a high chance that the phone could be gone but the only way to find out is by opening it up. The LCD itself could be gone and maybe the battery. No harm in trying as you have said the phone is already gone.