OK. I understand, I guess... Not really. Could you provide a little detail about your observations?
When you repeat that your "keyboard will not turn on," do you mean that no LED is visible although you're
sure the batteries' voltage, polarity, and seating are A-OK? By "seating," I'm wondering whether the contacts inside the keyboard's battery compartment are clean, free from oxidation, and unbent, etc. Do you have the capability to test the "in-place" voltage? If this kind of problem is involved — but isn't amenable to anything you try — then professional repair (or you "breaking into the case") would seem to be the next logical step...
Or, if it's that you
can see the light but "nothing happens" when you try to use the keyboard — then would you please explain your basis for concluding that "Bluetooth is not the problem" ?
I intentionally shared my experience with AppleCare, who provided a case number that facilitated replacement — for a situation involving a keyboard with power problems. From your reply, I don't really know anything further about your observations, objectives, and constraints.
If none of the ideas help and AppleCare assistance isn't feasible, I don't know how to be much help from written interactions at this distance. Although their subjects are different Apple keyboards, perhaps Byron Gracey's
Disassembly of an Apple Pro keyboard or Stephan Kurtz's "
USB Keyboard" websites may be of service to your efforts.
Otherwise, I'm afraid that service or replacement are the most likely options to succeed.
Perhaps I'm still not understanding the problem definition &/or what kind of help you're seeking. In any case, good luck.
Regards,
Dean