On my new iPad 3, when I push the home button to get out of a program, it does not work. I push & hold and nothing happens. I have rebooted the iPad several times, nothing. What should I try next. It seems to be frozen and does not close the program I am on.

Did you installed the latest IOS? Are you in the Beta program?
Try one thing, press and hold the power button and the home button together. Keep holding them until you see the Apple logo again, let go of them when Apple log is display. Hope it works.

Press and hold down the Home button on the front of your iPhone, iPod touch, or iPad while still holding down the On/Off button. Keep holding both buttons as the screen turns off keep holding both buttons until the turns back on again and displays the Apple logo

Have you tried doing a reboot? Hold down the lock button on the upper right corner, the. Slide to shut down. Then hold the lock or home button to reboot. See if that helps with your issue.

push the home button twice to bring up all active apps; swipe them all one at a time to the top of the screen, or, hold both the home and power button down for 10 seconds to force a hard shutdown.

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?

Try a basic reset. It will not erase anything. Make sure the device is not plugged in. Hold the home button & power button at the same time until you see an apple on the screen. This will reboot & relaunch the software. It solves a lot of these performance problems.

I’m happy to help further over the phone at https://www.6ya.com/expert/clint_f00dc48f472715e0

This tutorial will explain how to force your iPad to restart if it gets stuck or freezes up.
Forcing your iPad to restart will not cause any loss of data - with the possible exception of any work you were doing at the time the iPad and/or App froze, forcing you to restart it.

Click and hold down the Sleep/Wake button (located on the upper-right corner of your iPad). While you're holding down the Sleep/Wake button, hold down the Home button as well (located on the front of your iPad at the bottom). Hold down both buttons until your iPad powers off. It will reboot and start again with a small silver Apple image on the screen. It takes about 30 seconds for the iPad completely start up.

If you've got a locked up iPad app or otherwise misbehaving iPad, and want to reboot / reset your iPad, simply hold the sleep and home buttons together until the iPad restarts.
You'll see the shutoff slider come up first, but just keep holding. The screen will go blank and the Apple logo will reappear as the iPad reboots.
Note: this does not reset any data on your iPad. This is just a restart, equivalent to rebooting your computer.

If the iPad will not reboot using the standard "Hard Reboot" (holding the power button and home button until the iPad restarts.) then I would advise restoring the iPad using iTunes which will set it back to factory settings.