Hello, My name is ***** ***** will do my best to help you on this question.
Looks like you have already gone through few diagnostics by replacing the battery. From what i understand if the camera is powering on normally and you still don't see the screen powering up most certainly the LCD screen has gone bad either the connection or the LCD itself which will need a replacement. To confirm if that's indeed the case i suggest try powering up the camera and take few shots even with blank screen and then remove the memory card to see if the shots were captured if yes then 100% the issue is with the LCD screen otherwise could be more fatal issue with the entire camera.
If indeed the problem is with LCD which most likely is the case. You can either get it repaired/replaced which could be anywhere from 50$ to $150. Because this is a water proof unit i prefer you not spend that kind of money with potential issue with re-sealing in the future. Instead you might be better off buying a newer model relatively cheaper. here is one example.
I hope this information is helpful. Let me know if you have any further questions. Please don't forget to rate/accept this answer. Thanks and Happy Holidays.