I might be able to help. I have an older Apple Bluetooth Keyboard, Model A1314, and it’s a royal pain to get it to pair with a computer (after it’s paired the first time, though, it works great). If you have the same model or a similar one, here’s what you need to do:
1. Remove the batteries from the keyboard.
2. Slide batteries back into their receptacle, but don’t screw on the steel end-cap yet.
For the remainder of the process, you need to be holding down the power button firmly - do not release it until the keyboard has finished pairing. Doing all of the following while holding down the power button is awkward - I cradle the keyboard along my left arm, holding in the button with my left thumb, and that leaves my right hand free to type in the pairing code.
3. Screw on the battery cap - the power light on the keyboard will start to blink.
4. Go through the entire pairing process, inputting the pairing code using the top-row number keys and then hitting “Return” to complete. The keyboard should now be paired.
5. Only once pairing is complete can you release the power button.
After this, the keyboard should work properly. If you find that the keyboard says it’s paired properly but doesn’t seem to input text, it may have defaulted to “Number Pad” mode - hold down “Fn” and double-tap “F6” to put it into keyboard mode.
This ridiculous process is what I need to use for my Apple A1314 keyboard - I hope it works for you, too.