Cannot sign into Apple ID on iPhone

Recently I noticed that I was not able to download apps from the App Store on my iPhone 6s. I eventually got annoyed with it and tried to update my phone last night in attempt to fix it. I updated to iOS 10 (I was previously on an early version of iOS 9.) The update process was incredibly painful. Once it updated, it went to the "Welcome" screen where you have to set up a few things, like Hey Siri. It had me enter my Apple ID, and it would freeze after I hit enter. So I reset it and then it locked up on the Terms and Conditions. After I reset again it locked up on the "Updating iCloud settings." Eventually I connected it to iTunes on my computer and it skipped all of those issues and just went to Hey Siri. So I was able to get into my phone after more than an hour. But now I'm having the Apple ID issue still. It kept asking me to enter my password over and over again, and it would just freeze after I hit "Sign in." I was able to finally log out of my Apple ID account on my iPhone, but now I cannot log back in. I've tried to also log out of my iCloud account to see if that would help, as I found a few things that said it might, but I cannot as it asks me to enter my Apple ID to disable Find My Phone. I've kinda hit a brick wall on what to do.
Long story short, my phone freezes when I enter my Apple ID password and try to sign in. I can hit the home button and lock button and it'll get me out of it, but it still won't sign into my Apple ID.
Thank you for any help.