Sign in to iCloud paralyzes iPad

I have had my new iPad Air 2 for two weeks. For the past two days I could not use it. As soon as I got it unlocked and tried to connect to my keyboard, a message would appear: "Sign in to iCloud." When I clicked Cancel the message came back immediately. I could not press the home button quickly enough before the message was back again. When the message was on the screen, the iPad was totally unresponsive. Today while I was trying again, the message went away and has not come back, but I'm afraid about the next time. I do not ever want to see the word iCloud again. What can I do next time?