Keyboard will not turn on, no green led lights up, no sign of damage

Hi, I have an outwardly perfect Mac wireless keyboard. However, I cannot get it to turn on (let alone pair with anything).

The on/off button moves normally, and there are no visible dents. I've changed the batteries to fresh ones, and I've even tried putting a bit of aluminum foil between the last battery and the end cap that secures the batteries in their compartment, just in case the spring was damaged and the batteries were not connecting properly.

I'm not aware of any spillages on the keyboard. I can only presume that there is something going wrong with the power management unit, or the on/off switch. Any suggestions ?