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That screen indicates that the firmware/system software of your iPad has been corrupted. Your iPad is asking you to restore the software from iTunes application on your computer.
First download and install latest iTunes application on your computer from here : http://www.apple.com/itunes/download/
Then you can restore it by putting it to DFU (Device Firmware Upgrade) Mode. DFU Mode is a mode which will allow you to restore your iPad to working condition. Follow the steps below to put your iPad to DFU Mode;
· Connect the iPad to your computer with the USB Cable.
· Open iTunes application on your computer
· On your iPad Press and hold the Home button and the Power button at the same time.
· After EXACTLY 8 seconds release the Power button. Continue holding the home button until your iTunes shows a message telling you that it has detected an iPad in recovery mode.
· Click OK or Restore
Note : Put it to DFU Mode while connected to computer and also in DFU Mode your iPad will remain blank or shows black screen. Timing is critical when you put it to DFU Mode, so keep trying until it goes to DFU Mode.
Remember : Your iPad won't respond when it is in DFU mode. That is normal.
Please let me know if that didn't work, so I will walk you through the steps.