Found the answer! This solution will work for most of this type of printer (with an electronic instead of physical power switch and a button that says 'Secure').
Ensure that the 'data' pending light is not flashing.
Open the top lid of the printer and leave ajar.
Press both the “Secure” and “X Cancel” buttons together. Hold them together if needed.
In the case of the HL-L5100DN, just press 'OK' on the first item listed 'TNR-STR'
Or use the arrow keys to select the cartridge model you would like to reset and press “OK”.
Press the UP arrow '+' to select 'Reset' of the the cartridge.
Once reset is selected you will see “ACCEPTED” on the screen.
Phew! I can print again.
Kenneth