Which model of keyboard is this, because my A1255 doesn't disassemble like this - the battery terminal is solidly restrained inside the tube by means of a metal expansion ring. Doesn't seem user repairable :(

I had this keyboard fail on me, and the 'ball of tin foil in the battery compartment' didn't work.

The grey plastic pops off with a small screwdriver - 6 clips hold it in place.

Re: the screw that’s at the ‘button’ end. Remove the screw, then you remove the ‘pole’ that the screw went into (it unscrews too). This will allow you to remove the board (it’s a squeeze, but you can pull it out) - you might need to push in the white plastic beside the button wall to allow you to get it out.

I was unable to non-destructively remove the internal battery terminal. The metal expansion ring which holds it in place appears to be the most well-made part of this entire £59 keyboard :( Only way I found was to knock it through forcefully with a long screwdriver - from the 'internal' end, out through the battery hole. The red wire became disconnected when I did this. It was connected to the point that sticks out the bottom of the battery terminal. Black wire connects to the expansion ring.

Good luck