Battery door metall batterry connectors fell out
When you can't close the battery door as it should be closed, you can't turn on the camera. In almost all digital cameras there is a protection switch, that prevents the camera to work, with an open battery door, because the camera could stop any moment when the battery comes loose. When the camera was accessing the memory, when it falls without power, the memory can be damaged and you could loose all the pictures saved on the memory card.
I'm afraid, when the battery door came out, some things are missing, like a spring, axel and perhaps some other little metal or plastic things. To come out, some mechanical damage must be there, so it won't be easy to reinstall the door yourself.
Bet thing you can do is show it in a service centre and ask if it can be repaired and what it will cost.
Service manuals, with pictures about all parts, are only sold to approved repair centres.
The only chance to find anything, is on ifixit dot com, because they have manuals and videos of lots of electronic stuff for free.
Repair over there is on your own risk.
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