My account was hacked and used for cheating and was permanently banned.

[lord of random insult]

My account was hacked and used for cheating and was permanently banned.
I can provide email reminders for remote logins.

[datCookie]

This isn't Steam Support.

Note: Your account is highly unlikely to be unbanned from what ever game you're banned from

[miamew3]

2522 day(s) since last ban

[Vamp]

1. the account was not hacked, it was hijacked.
2. after the owner was careless with his password
3. probably due to visiting skin trading sites or falling for one of those lame scams
4. took you long enough to notice that it was banned, sounds like a bought account.

[Chika Ogiue]

Account security is your responsibility. As is any actions taken within games. Any bans applied to your account are highly unlikely to removed because you lost control of your account. But you can try reaching out to the publisher / developer if it's not a Valve game. If you were banned in a Valve game, the ban is permanent.

[videomike_Ultimate_Plushie]

Sorry, but you're screwed. Assuming you're not lying, there's nothing you can do. Keeping track of who isn't on your account or not is part of the internet, and if we wanna keep any kind of anomynity, even in concept, thats how it has to be.