Try rebooting the iPad if you are stuck on a screen and can't get out of it.
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 - let go of the buttons.
Try a reset by pressing the home and sleep buttons until you see the Apple logo, ignoring the slider. Takes about 5-15 secs of button holding and you won't lose any data or settings.
If still a problem restore with your backup.
If still a problem restore as new, i.e. without your backup. See how it runs with nothing synced to it.
If still a problem, it's likely a hardware issue.