It is difficult to say without being able to inspect the device myself, best case scenario the lightning port flex cable needs to be replaced which is why the computer is not recognising it. This is a simple job which any repair shop should be able to do for you. Otherwise there may be damage on the logic board which can either be cleaned with isopropyl alcohol (again any repair store should be able to do this) or it may need some micro soldering work to recover the data which is quite a bit more tricky.
My recommendation is to take it to your local repair store and get them to inspect the device to see if they can recover the data by cleaning the board and replacing the flex cable. Make sure you stress that you want to recover the data and not restore the device!!. If that is unsuccessful then you could try sending it in to iPad rehab (http://mendonipadrehab.com) or somewhere similar to see if they can recover the data for you.