Unlocking lockscreen without a keyboard

Have you charged the Bluetooth keyboard or replaced the batteries lately?

If the Bluetooth keyboard is not connecting to the iMac, then you will have to use a wired USB keyboard to enter your password and access the iMac. You can buy or borrow most any wired USB keyboard. Even a PC keyboard will do.

The following will require any USB keyboard and 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 Start up your Mac in safe mode - Apple Support

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. 

Did you try to connect the keyboard by the cable?