My kindle has started refusing to start up once it has been closed down. I have to connect it to the computer, when it starts OK, but then, when it closes, the same problem occurs.
have you made sure that it's completely charged (light is green)?
have you tried a reboot by holding the power button in for a full 30 seconds?
are you using a cover? If o have you tried removing it from the cover and using the power button to turn it on?