See if the iPad will startup if you reboot.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.Or look through here for more help.iPad (3rd gen) Wi-Fi, iOS 6, 64GB WiFi
I already tried this, but after reboot the screen looks the same, only the Apple logo, even I let it there by a couple the hours and the same... I tried connecting to iTunes but it didn't work, it shows a message that the iPad has a Password but as I mentioned the iPad screen doesn't show the Password request...
Try and force the iPad into Recovery Mode
1. Disconnect the USB cable from the device, but leave the other end of the cable connected to your computer's USB port.
2. Turn off the device: Press and hold the Sleep/Wake button for a few seconds until the red slider appears, then slide the slider. Wait for the device to turn off.
3.While pressing and holding the Home button, reconnect the USB cable to the device. The device should turn on.
4. Continue holding the Home button until you see the "Connect to iTunes" screen. When this screen appears, release the Home button. iTunes should alert you that it has detected a device in recovery mode. Click OK, and then click Restore to restore the device.
Note: Data will be lost. You may have to repeat the above many times.
Thank you! This solved the problem, the iPad is complety restored, anyway is better than having the issue.
I made the steps twice, and in the second, it showed the message of the password, I selected cancel, but it continued with the software update and restoring.
Just a last question, why this problem happened? (My original post)
Thanks a lot !