Oh also- I try those same batteries that the keyboard wouldn't sync with on other devices (e.g. an old AA battery powered Digital camera and it shows that the batteries have full power.
I have an add one here. I have a Microsoft Wireless Keyboard 6000 v3.0 with AA batteries that are obviously low on juice. I try and swap them out for brand new EverReady batteries, and they don't work (I used 20 different combinations of the entire pack of 8. I i use rechargable AA Energizer battery, and they don't work. No matter what troubleshooting I do (different USB ports, syncing via the button, etc), I get no response.
I plug in any combination of the three failing Duracell batteries, and it instantly works and syncs (although has shoddy connection issues).
What the heck?