Q: iMac won't recognize Bluetooth keyboard

I just had to buy a new iMac and I want to use the Bluetooth keyboard from my 2010 iMac, but Bluetooth won't recognize it. Here's what I've done: 

- I've taken the batteries out of the new keyboard and removed it from the house. 

- I took the batteries out of my original keyboard (same model) and let it sit for a few minutes, as instructed by the Apple dealer here. (The computer it's paired with is gone due to a dead logic board.)

- I used the Bluetooth menu on the top menu bar to connect the older keyboard.  It very briefly showed it connected, then went back to searching and said no keyboard detected.  The green light was flashing on the keyboard at the time.

To answer the inevitable question - I don't want to use the keyboard that came with this iMac because the chemical smell it's emitting makes my eyes burn and is too repulsive for me to work with it.  I'm currently using a clunky old extended USB keyboard just so I can work.

Any help or advice would be greatly appreciated!

Thanks, Carole