My old wired keyboard works fine. No damage is visible. New batteries don't help. It connects to my iPad just fine, but not the iMac running OSX10.8.5 Mountain Lion. in System Preferences>keyboard> Bluetooth keyboard search does not find a keyboard. Wireless mouse works fine.
iMac, OS X Mountain Lion (10.8.5)
First make sure the batteries aren't dead and that the keyboard hasn't already been paired with another device. If it hasn't, the keyboard should pair automatically when you reboot. You may have to press and hold the power button on the right side of an Apple keyboard until the LED starts flashing.
Otherwise see these support articles:
Apple Wireless Keyboard: Difficulty during pairing process
Unreliable wireless performance may occur when USB 3.0 external devices are close
First make sure the batteries aren't dead and that the keyboard hasn't already been paired with another device. If it hasn't, the keyboard should pair automatically when you reboot. You may have to press and hold the power button on the right side of an Apple keyboard until the LED starts flashing.
Otherwise see these support articles:
Apple Wireless Keyboard: Difficulty during pairing process
Unreliable wireless performance may occur when USB 3.0 external devices are close
iMac suddenly fails to recognize my Apple bluetooth keyboard
