My iPad 4 is working on its own without touChing it. It will closing and opening applications on its own. the following were the steps taking in trying to fix the problem 1. I have restarted it several times 2. I have removed the SIM card 3. I switc

Go through these steps in order.

Close all apps. Press the Home button two times quickly. You'll see small previews of your recently used apps. Swipe left to find the app you want to close. Swipe up on the app's preview to close it. Close all apps this way.

Force restart your iPad. Not data is affected. To force restart your device, press and hold both the l/Wake and Home buttons for at least ten seconds, until you see the Apple logo.

If that didn't help, Reset all settings. You will not lose any data, but all of the device settings will have to be entered in the settings app again, including WiFi network passwords. Settings>General>Reset>Reset all Settings.

If all of that fails, restore the iOS software. Backup your iPad before you restore, then restore the backup when you are done. If that still doesn't help, restore your iPad as new and start all over again. Most purchased content can be downloaded again at no charge as long as you use the same Apple ID and as long as the content is still available in the store.

Restore iPad to Factory Settings

http://support.apple.com/kb/ht1414

Download Past Purchases

http://support.apple.com/kb/ht2519

If you restore as new and it is still misbehaving, make an appointment at an Apple Store and ask them to evaluate it for hardware problems.

Then take it back to whoever replaced the screen and have them fix it again. That's where your problem is I'm sure.