Q: For days now, my iPad Air has insisted that it cannot connect to iTunes. The wifi works fine for apps and other devices, and I've tried all the suggested options on the support page. Nothing has worked. What do I do?

The timezone is correct, it's signed in through 'iCloud' in settings, and all the apps still work relatively fine, including those which require internet, so the problem isn't the internet. However, the iPad Air no longer will connect to iTunes, making it impossible to update anything. It won't let me log back in through 'iTunes and App Store' in settings, just telling me again that it cannot connect to iTunes whenever I attempt it. I've also noticed that Game Center is acting strange, its page in settings won't even load and it often delays signing in when I open an app compatible with it. My iOS is up to date, at 9.3.1. The only thing I can think of is that I had to change my password recently, but it had me log in with the new password on the device, and this problem didn't show up until a few days later. I'm at a loss on what to do at this point, and I've already tried all of Apple support's suggested fixes. Are there any less-known fixes that might resolve this issue? Or, is this a wide-spread problem Apple is having right now with their servers?