Verification Failed - Error connecting to the Apple ID Server

I just installed iOS 9.3. I did this against my best judgement because it seems like every time I update things get WORSE, not better.
My phone won't allow me to sign into my Apple Id account.

I start my phone and get a message that says: "Apple ID Verification. Enter the password in Settings"
After I enter my Apple ID Password I click 'Sign In' and nothing happens. It just freezes. If I hit a few keys a message pops up that says: "Verification Failed. There was an error connecting to the Apple ID server."