Apple wireless keyboard goes into numlock mode

I don't understand how this happens, since the silly keyboard doesn't even have a numlock, but occasionally I find that my iMac wireless keyboard only seems to have a few keys working, mostly on the right side. For a long time, this happened only when I would reboot the machine, so that the only thing I could type was a login password, which of course I cannot see.

This finally occurrred while already logged in one time, and I noticed that the keys that DID work were producing numbers instead of the letters they should have. I immediately recognized that this was numlock behavior, and set about trying to figure out how to turn it off so the keyboard would work again.

No dice. Fn-F6 does not work to turn it off, it just gives me that error bloop sound. Disconnecting or turning off the keyboard doesn't help. Switching to another user doesn't help. It's just stuck in numlock mode with no way to turn it off.

This is under warranty so I called Support and got someone who was obviously quite a junior tech. After some very wimpy troubleshooting his best guess was to reinstall the OS! I said thanks anyway and I would call back later.

I think it's certainly possible there's a hardware issue here, and an OS reinstall is just an extreme measure, as well as a cop out. I've just recently reinstalled the OS from scratch anyway. So, anyone else have any ideas how it gets into this state, and how to get it back out? Thanks...

/mike