Need Diablo 3 Account Help!

no you cant, open a ticket at their support site, they'll help through procedures to recover it

Anyone can use the installer file to put their game on the computer. So, to answer your question, no - merely having the gamed installed does not prove you bought it. The proof of ownership comes when you actually log into the game server with a valid account.

If you really do have an account that was compromised you should be able to retake control of it by resetting your password just like you do with anything else. If the account is locked you will need to speak to Customer Service (good luck) about the issue and see if they can help you.

That aside the whole situation smells fishy to me so I'll just say this.. if you were banned for cheating in some way you will not get your account back so go buy another copy and stop cheating. If you were hacked shortly after starting you either have a really crappy password/shared your account/used the same username and password on a shady site/malware feeding someone your information, or any of the other obvious reasons why your account would be hacked. Also, not to be a troll, but get an authenticator.