keyboard will not work

I didn't realize your have such an old iMac. It helps to know these details in your original post.

You can plug any USB keyboard to verify if your keyboard has failed. Yes, you can purchase a new Apple wireless keyboard for your 2012 iMac as long as it is the keyboard meant for the Intel-based iMacs which you have. Do NOT purchase then new keyboards meant for the new 24" iMac as that has touch-id and it is not meant for Intel-based iMacs.

This Apple keyboard should work with your iMac if you want to go this route. Worst-case you can plug in the included cable and make it a wired keyboard. Or you can purchase a myriad of generic USB keyboards as well.

Magic Keyboard with Numeric Keypad for Mac models - Apple

Plug your keyboard to your iMac using the included USB->Lightning cable. It's possible your keyboard's battery is dead and if so, the cable will not only charge the batteries, but it will also treat your keyboard as a standard, wired keyboard in the meantime.

Also, if the wireless connection has failed for some reason, plugging it to your iMac with a cable also has the benefit of automatically re-pairing it to your Mac.

Obviously, make sure your keyboard is tuned on as well.

Are you using an Apple-branded keyboard? If not, you may have a keyboard failure so you should try another keyboard to verify.

Also, use a different USB port on the back of your Mac.