Pulled battery and actually let it sit overnight. Still no joy. It boots up but then won't let you turn it off via the power button (long press).
I have virus software, but it says there is no virus. Another thing that is weird is that when the screen is off it still makes clicking sounds on its own. It's the same clicking sound that you hear when you are turning the phone on/off. It does this completely on its own, randomly, every now and then.
I just tried to shut it off and it got as far as the 'Android' screen for a moment and instead of continuing to shut down it started back up again and went to the lock screen. It stayed there for a minute and then logged itself into the home screen, all without any human intervention. It also will move from the home screen to other various other screens all on its own. That's why I thought that if there was a good diagnostic software that I could run on the phone, that it could point me in the right direction as to what is wrong.