You need a registered and validated forum account at http://forums.dota-allstars.com/ in order to use this site. If you don't have an account, go there and register. You need to use your forum username and password to login here. Your battle.net username and password will not work.
If it doesn't work, you should double check that you have the correct username and password by trying to log in on the forums.
You need to set your battle.net name in the forums to the name you need unbanned, and you need to set the realm to "Azeroth". We use this data to map forum usernames to TDA usernames.
To change these values, go to the forums and select My Controls at the top of the page. Then, find Edit Profile Information along the left side of the page. The BNet Name and BNet Realm are the first two options. Set BNet Name to your battle.net username, and BNet Realm to "Azeroth".
If you've done that and it still doesn't say you're banned, you should doublecheck that you're banned. If you were simply kicked from the channel, you can rejoin immediately. If you were timebanned, you should wait for the time to expire. In these cases, you should find out why you were kicked or banned from the moderator who kicked or banned you. You only need to file an appeal if you were blacklisted, generally as a result of in-game conduct.