It is really going to depend on if it is actually still working and if it will allow you do access info.
Most phones will ask you to choose an option when connecting them to a computer via USB cord, on the phone itself. If that is the case here, meaning you have to tap something on the phones screen, then that could be an issue. Unless the phone still has sensitivity, just not a display. Which does happen.
If you can get it to connect to a computer, and get the phone to allow you to view the internal memory of the phone through folder on the computer, you should then be able to get anything you have on the phone off of it.