The advice on how to submit a ticket to appeal a ban is correct. They do not accept appeals over the phone.
If you feel this was the result of a compromise then you also will want to secure your PC and your account.
1. Download, install, and update Malwarebytes (free version is fine). Boot into safe mode and run a FULL (not quick version) scan with the game up and gibberish in the login fields. Some malware only activates under those conditions.
2. When that scan is done, run a FULL virus scan with an updated virus scanner. Microsoft Security Essentials is free and decent these days. Some folks here also like Avast. Better than Nortons, MacAffee, etc.
3. From a PC you know to be free of malware, change your email password because hackers often get into that too. Check it for forwarding as well. Sometimes hackers set up forwarding. Change your bnet password again now that the PC is clean.
4. Create a new email that you use ONLY for battle.net and switch to it. Gmail is great because you can put two factor authentication on it and prevent hackers from logging in without a code.
5. Get an Authenticator!!!! The mobile device version is FREE and the keychain is only $6.50 in the US with free shipping. (unfortunately the store does not currently have them for sale though ) https://us.battle.net/support/en/article/battlenet-authenticator
6. Consider SMS Protect - this is not an Authenticator, but is a messaging service that lets you know about account changes and prevents some of them, such as an unauthorized email change. https://us.battle.net/support/en/article/battlenet-sms-protect