There are few diagnostic procedures for the iPad.
Stop all apps. ( Double tap home button. Drag up. ) Look at what process are running. This would be the base line. See what processes start with each app.
Backup and restore.
look at logs.
visit apple store.
I'd see if you can find the log files. Perhaps you can find what app started the process. Should be identifiable by full path.
With ios, you need to attach you iDevice to a computer to read the logs. See:
http://support.kioskproapp.com/knowledgebase/articles/310940
http://bjango.com/help/crashlog/
http://stackoverflow.com/questions/4242780/ipad-how-to-get-crash-report
https://developer.apple.com/library/ios/technotes/tn2151/_index.html#//apple_ref /doc/uid/DTS40008184
Re-boot ipad.
Press and hold the Sleep/Wake button until a red slider appears, then drag the slider. Then press and hold the Sleep/Wake button until the Apple logo appears. page 128 iPad user manual.
force power down if the above give you trouble.
Hold down both the Sleep/Wake button and the Home button. Ten seconds or more. Hold until the Apple logo appears.
more details on re-booting:
http://ipad.about.com/od/iPad_Guide/ss/How-To-Reboot-Your-iPad-Power-Off.htm
Restore to factory settings by loading the latest version of ios that your machine will support:
Do a full backup of your device. Twice is best -- cloud and computer.
"You can use iTunes to restore your iPhone, iPad, or iPod touch to factory settings and the latest version of iOS."
http://support.apple.com/kb/HT1414?viewlocale=en_US&locale=en_US
"You can put your iOS device into recovery mode, then restore it using iTunes.:
http://support.apple.com/en-us/HT201263
At last resort you could consider DFU (Device Firmware Update). This could void your warranty.
http://www.imore.com/tip-put-iphone-ipad-dfu-mode
nsdjoey explains how to force a reload of ios
https://discussions.apple.com/thread/7067914