When restoring the database, you needed to create a new database, and you gave it credentials for an user, as explained in our wiki, with something similar to this:
grant all privileges on database_name.* to 'root'@'localhost' identified by 'USER_PASSWORD';
You used root as user, and we use to use another one. Moreover, the password can be a different one from the one we use. My suggestion:
Delete the database in your new server to start from the beginning.
Go to YOUR_INSTALLATION_DIRECTORY/apps/mantis/htdocs/config_inc.php file and check the values of
g_db_username, g_db_password and g_database_name.
Create your database again, using g_dabatase_name as database_name.
Then give access to the user g_db_username with password g_db_password, using something like
grant all privileges on g_database_name.* to 'g_db_username'@'localhost' identified by 'g_db_password';
(Using your own database name, database user and database password)
Restore your backup.
Restart the servers.
It should work now!