iMac v. Bluetooth

Check these basics first:

1. Is Bluetooth turned ON in system preferences?
2. Do you have fresh batteries in the keyboard & mouse? Are they inserted the correct way?
3. Once the Mac is on, press the round button on the upper right side of the Apple keyboard to initiate connection
4. Make sure the mouse is turned on (slider switch on the bottom of the Apple mouse)

If it's an Apple mouse, there is a small, rectangular black slider on the bottom of the mouse. That's the latch for the battery cover.

Also on the underside of the mouse, there is a separate, tiny, round on/off switch near the front, next to the optical lens. Make sure it's pushed forward to turn it on. If you can see green in the space where the switch is, it's on.

One other suggestion I'd make is in System Preferences > Bluetooth > Advanced turn on the options to have Bluetooth Setup Assistant run if the iMac doesn't detect a keyboard or mouse upon Startup.

One thing I found that has worked is the following:

The following will require any USB keyboard an mouse. If you don’t have them, borrow or buy them, they are inexpensive!

1.     Connect the USB keyboard and mouse to the computer.

2.     Open System Preferences – Bluetooth

3.     Un-pair the wireless keyboard and mouse.

4.     Turn off Bluetooth

5.     Restart the computer in Safe Mode per the directions in https://support.apple.com/en-us/HT201262

6.     Restart the computer normally.

7.     Open System Preferences – Bluetooth

8.     Turn on Bluetooth

9.     Re-Pair the wireless keyboard and mouse.

10.  Unplug the USB keyboard and mouse and begin testing the wireless devices again.