I'am not atlking about ispconfig users, I talk about mysql users. The ispconfig installer creates a mysql database user name ispconfig and I guess that you have overwritten this user by copying back the old mysql database. The problem that this causes now is that neither the ispconfig nor services like postfix, pure-ftpd or dovecot / courier can connect to mysql anymore.
Please open the file /usr/local/ispconfig/server/lib/config.inc.php, in this file you find a mysql password. This is the cleartext password of the mysql user. Copy this password (do not chnage it in that file!), then open the mysql database with the name "mysql", find the user table in that database, there you will find a user named "ispconfig". Change the password for that mysql user to the password that you found in the config.inc.php file. Select "password" as encryption method. And then reload or restart the mysql database.