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You would need to replace any of the toners that have run out for the printer to work correctly, otherwise you will get an error message. This is because the colours are actually used to print black depending on the shade of black.
There is potentially a way of getting the printer to print, providing that all toners are inside the printer and you've installed a new black cartridge. Take out each colour and rock it from side to side, then reinstall them. Often the toner gets stuck inside the corners of the cartridge and rocking it loosens it up a bit so they last longer.