Just tried logging in, get message “Due to suspicious activity, this account has been banned.” What suspicious activity??? I have never used a bot, never used any map hacks, 3rd party software, exploits, cheats, etc… I recently moved to a different state and the email associated with the account is no longer active but my phone number is still the same. What in the hell is going on?
I was able to play no more than 2 hours ago as of this writing.
That is not a ban. That is a security measure that locks the account when it detects a login from a strange location or device.
Normally all you have to do is reset your password from the current device you are on. Doing that requires email access and such so only the account holder should be able to do it.
If you are traveling, one way to reduce security lockouts is to use the Blizz Authenticator. It is a bit more complicated now though, you don’t just need a device that can run it, you need a phone number that is not VOIP or pre-paid (or Cricket).
If changing your password does not work, you can put in a ticket. However, those are running REALLY high time wise right now due to a massive ban in OW and WoW.
You did nothing wrong though. Breathe 
They are trying to keep hackers out of your account.
It’s working now. My phone is pre-paid (tracphone) and it works. Still not sure why it won’t let me change my email info. Old one is no longer active and when I try to change to my gmail account it pops up "email already in use’.
It just did it again. C’mon, Blizz, it’s ME - not some hacker. I moved from AR to LA but my phone number and password have not changed. Fix this! 
I have the same issue. However, I cannot access my old email address and I did not put a phone number on the account. I tried submitting a ticket and they said I would get a response within 24 hours, but that never happened. I can’t find a phone number or live chat to ask for help.