I have a Phantom 3, not 4, but I think my answer is relevant either way. Unfortunately I don't think there is much you can know as to the extent of the damage until you fire it up and fly it some more, which you say you have already done. If it were me, I would plan my next flight around starting it up and just waiting a few minutes to see if all systems are definitely coming online normally. Then start the motors and do the same, just wait and watch. Are you keeping satellite connection, fpv connection, camera recording properly, etc. Then go into a low hover and do the same. Do a short, low & slow flight to see that everything is still running correctly.
Phantoms are known to survive many crashes pretty well, I have had a few tumbles myself. Actually my last was just like yours. Clipped a wire and flipped it, landed right side up but hard, then off into a yard and bush upside down. Dinged one prop beyond use but other that that it was just like nothing ever happened.