Would it be possible to sue Blizzard for unfairly banning my account?

You can sue anyone for anything. But in this case you are unlikely to win. Blizzard is a private company. They are under no obligation to treat you fairly. If you buy a service and they cancel that service, then normally you would at most be entitled to a refund. But most online sites have a contract which is typically called “terms and conditions” posted on their website. (I have drafted many of these contacts myself for clients.) You must agree to this contract in order to use the site. Although I personally do not think these contracts meet the conditions for enforceability, the courts do. Except for some very extreme terms, the courts will enforce the contract. It did not take me long to find Blizzard’s terms and conditions and find this clause which is probably binding on you. 7. ACCOUNT SUSPENSION/CANCELATION. BLIZZARD MAY SUSPEND, TERMINATE, MODIFY, OR DELETE ACCOUNTS AT ANY TIME FOR ANY REASON OR FOR NO REASON, WITH OR WITHOUT NOTICE TO YOU. Accounts terminated by Blizzard for any type of abuse, including without limitation a violation of these TOU, a Game-specific Terms of Use, or a Game EULA will not be reactivated for any reason. For purposes of explanation and not limitation, most account suspensions, terminations and/or deletions are the result of violations of these TOU, a Game-specific Terms of Use, a Game EULA or other Blizzard policy. Most of these websites are specifically designed to make it difficult for the use to reach a real person and get a personalized response. You may be able to harass them enough through emails and complaints online that they will give you a refund. But under the terms of the contract you allegedly agreed to, they probably do not have to. I know this can be very frustrating, but that is the way it is.