fn doesn't work on new keyboard with old iMac

I paired a new short keyboard that came with a new iMac to my old iMac6.1 and it works perfectly except that the fn doesn't seem to work at all. For instance, fn+Delete just deletes to the left, it does not forward delete; fn+F11 just shows the desktop, it does not lower the volume.

Any ideas on how to get fn to work?

Background: My wife got a shiny brand new 21.5" iMac just today. She did not like the short keyboard. So I took the full sized keyboard with the numeric keypad that came with my old 24" iMac6.1 and paired it with her new iMac. I paired her brand new short keyboard with my old iMac. All the keys work, except apparently not the fn.

I've been through the support articles.

Speak selected text is off.

Slow keys and Mouse keys are turned off.

Keyboard viewer does not show the fn key at all.

"Use all F1, F2, etc. keys as standard function keys" is off but the behavior doesn't change whether this is on or off.