Persistent blank screen which won't turn off or on.what should I do?

Have you tried a reboot by holding both the power and home buttons until the apple logo appears and it restarts, if the red slider appears ignore it.

Frozen or unresponsive iPad

Resolve these most common issues:

• Display remains black or blank

• Touch screen not responding

• Application unexpectedly closes or freezes

http://www.apple.com/support/ipad/assistant/ipad/

iPad Frozen? How to Force Quit an App, Reset or Restart Your iPad

http://ipadacademy.com/2010/11/ipad-frozen-how-to-force-quit-an-app-reset-or-res tart-your-ipad

What to Do When Your iPad Won't Turn On

http://ipad.about.com/od/iPad_Troubleshooting/ss/What-To-Do-When-Your-Ipad-Wo-No t-Turn-On.htm

iOS: Not responding or does not turn on

http://support.apple.com/kb/TS3281

iPad: Basic troubleshooting

http://support.apple.com/kb/TS3274

 Cheers, Tom 😉