Hi, there could be a number of reasons the Kenwood dishwasher is dead (no lights shown), which include a lose connection, short circuit, failed switch or a main board failure.
To rule out a short circuit I would take the 13A fuse in the plug and put it into another appliance to check that replacement fuse hasnt blown, if that to has blown this would suggest a short circuit and require the unit to be stripped down to detect what is causing the short.
However if the fuse is working, and your confident the extension lead\socket the dishwasher is using is live, it would most likely suggest a main board failure which is around £75, plus £50 to fit, but it could also be a failed switch which is a £10 part.
Please let me know how you get on checking the fuse, and I will see what more we can do to narrow down the faulty component.
It appears in your response advising you tested the fuse and it worked, you created a second question so I have passed the duplicate to customer services so you are not double charged.
With regard to to the dishwasher, when you press the power button with it plugged in do you see the lights come on (even for a brief moment), I would try tapping the button to see if you can get the display to flash, if it does this would suggest its the switch at fault.
Please let me know how you get on.
This sounds like you will need an engineer visit as the fault is most likely to be the control board.
Please let me know if I can be of any further assistance.