New iPad 2 very erratic. Screens go on and off on on their on and more. Anyone have this problem and if so what is the solution?

Can you give more details? What are you using or doing when this occurs? Does it go back to home screen? The more info you can give...the more likely someone here can help you.

Try a hard reset:

Hold the power button and the home button down at the same time until you see the Apple Logo.

Let it reboot ~

Ok I will try to describe in more detail which is very difficult considering all that was going on at the same time. The last episode occurred while I was attempting to perform a soft reset. From the settings page with my hands off of the iPad the cursor would jump from subject to subject then stop on one and go through the entire area. Then it would stop and the search window would open and random letters/ numbers would enter in the window and then cursor would continue to do the same over and over. It did all of this on it's own with no input from me---the battery was about 40%-I placed it on charge overnight and this morning it's performing normally with no issues. Any ideas on what is going on with this thing? I think it's possessed.