If neither the ActivBoard nor the projector has power, then it is likely there a problem with the mains supply to the whole system. Both projector and ActivBoard feed from the same mains cable. Try plugging the ActivBoard+2 mains cable into a different mains wall socket.
If the projector has power but the ActivBoard's LED in the top left corner is not lit, then the issue is likely to be with the ActivBoard power supply. Trying another power supply from a known-working ActivBoard will determine if the issue is with the power supply or the DC cable.
As the power supply is no longer available to purchase from Promethean, please contact Promethean Technical Customer Support to check whether a solution is available.