I just ran into the craziest problem where I couldn't get any third-party apps on my iPad to open. I'd tap them, there'd be a quick blink, then nothing, I was back to the home screen with all my app icons.
This happened immediately after I had a problem with the YouTube app on my iPad. It quit working, then gave me an error message that was something like, "You do not have permission to access the requested resource." I rebooted my iPad, but still none of my apps would open. I was concerned my iPad had been hacked somehow, so I shut it off while I searched for a solution on another computer.
The solution is pretty crazy: Turn your iPad or iPhone back on, use it to go to the App Store, and install a free app -- any free app. After it's installed, go back to your other app icons that wouldn't start, and amazingly they suddenly work.
I don't develop apps for the iPad or iPhone (technically the iOS operating system), so I don't know why this works, but I read about it on the Apple discussion forums, and sure enough, it works.
So, if your iPhone or iPad has this problem where apps won't open (won't start), give this solution a try. It worked for me, and I hope it works for you also.