You CAN NOT be UNBANNED on ANY CS 1.6 server. It is impossible.
SteamID change is possible but this process doesn't provide you "unbanned". If an admin bans you, your SteamID and IP is being banned. You disconnected from server and you used SteamID Changer (steam_set_id 111) and when you try to reconnect server, you can not join because at the same time your IP is being banned. You need to renew your IP by turn off router and wait 2 minutes for take new IP. Or use VPN and change your IP in seconds but this time your connection will be so slow if your internet isn't speedy.
Don't look for this issue on the internet and other forums. Don't spend your time with this because there is no website, forum or person provides this.
Have a good day.