Try plugging it into a different outlet and using a different charging cable. If that doesn't help, please reach out directly to our Kindle team (click here) so they can pull up your account and device details and assist.
Well tried everything to get my Kindle paperwhite to turn on, different leads, sockets,holding for hours multiple times but no joy. Unfortunately it is dead :( But thank you to Sankar S in customer services who did give me 15% off a new one. So all sorted :)