Can you not attach the loose clip back to the frame? Gently pushing it into place, perhaps with the help of a not too sharp tip of an object should do. Or is the clip or its counterpart on the frame broken?
You can easily test whether the actual button on the core module works with the case taken off the phone.
If the button on the core module works, and if the button holding part on the frame is intact, you could swap the button parts of the power and camera buttons of the frame, if you want …