The CDTV keyboard does not work with A4000 without modification.
To get a black keyboard, you can simply change the wire to one from an A3000/A4000 keyboard. They have the same connectors inside the keyboard.
Unscrew the keyboards. Make a note of connector orientation (they might be keyed I cannot remember). Unplug cables, swap them over. Downside: the cable will not be black.
Alternatively you could re-wire the connector inside the cdtv keyboard. The connector is crimped so it may need a bit of effort to remove and re-wire.
