My ipad is showing the itune logo and the plug

You need to plug your iPad 2 into the computer that you normally use for backup.
This logo indicates that your iPad is in 'Recovery Mode'

You will need to reset your iPad. If you have a previous backup of your device on your computer, you can restore your iPad from that, otherwise you will need to plug the iPad into your computer and reset it.

Here's a solution for iPhone. I think it also works on your iPad.
How to Recover Data when iPhone Gets Stuck on iTunes Logo

you need to connect the iPad with an USB-cable to a computer and open iTunes software. there you will see your iPad showing up and you can do a restore:
Restore iPad to new factory condition

As for unlocking iPad, there are several ways you can resort to. Just follow one of them as below shows.

If you've neither synced with iTunes nor set up Find My iPhone in iCloud, you'll need to wipe your iPad to factory setting to remove the password, which means you'll suffer losing all your data on iPad and get it as a new one.
Please pay attention there is a slight difference in putting different models of iPad into recovery mode.
iPad Air

• 1. Turn off your iPad Air, press and hold the Home button.
• 2. While holding the Home key, connect the USB cable to the device. Wait until the Apple logo appears and keep holding the Home button for few more seconds.
• 3. Continue holding the Home button until the iTunes logo appears.

iPad mini/iPad pro

• 1. Connect your iPad to your computer or laptop and open iTunes.
• 2. While your device is connected, force to restart it.
• 3. Press and hold the Sleep/Wake and Home buttons at the same time. Don't release when you see the Apple logo. Keep holding both buttons until you see the recovery mode screen.

Now you have entered the recovery mode, and

1. When you see the option to Restore and Update, click it.

2. Wait for the process to finish. Then you can set up and use your device.

For more methods, check: How to Unlock iPad?

You need to connect the iPad with an USB-cable to a computer and open iTunes software. there you will see your iPad showing up and you can do a restore:

Restore iPad to new factory condition

You need to connect the iPad with an USB-cable to a computer and open iTunes software. there you will see your iPad showing up and you can do a restore: Restore iPad to new factory condition

If you are near an Apple store, take it to them. Most of them are very generous in helping users out with their issues; many times even when out of warranty. This will likely be your most efficient method in getting things straightened out.

You haven't given nearly enough information for specific ideas on what to do first. Is the iPad working when not plugged in to the computer? If not, what happens? Can you update your iPad via WiFi or 3G? There are many helpful websites that give you multiple ways of restoring your iPad, but unless we know exactly what is happening and what your end result should be, the best I can do is point you to:
https://www.google.com/search?q=restore+ipad+to+factory

Try reseting the iPad by holding the home and power buttons simultaneously until the iPad completely shuts down and the Apple logo appears.


Once the Apple logo appears you can release the buttons. If this does not work, you may need to connect your iPad to your computer and do a factory restore using iTunes.

When your Ipad Plugged to Itunes
It show's You This New Menu On Itunes