1) If your MySQL-Server runs on Linux you'd have to "unbind" the Address the server listens to.
Per default after a fresh install the server listens only to localhost.
At least, that was one of two problems this saturday for me.
No idea though for MySQL-Server on Windows.
2) On the MySQL-Server you have to allow the users to connect from a remote host.
Even the "root"-User is defaulted to "localhost" meaning: even if you use the correct login of Root with its password, if you try to connect from, say, "myLANPC01" to the MySQL-Server on "mySQLServer01", and you've not setup the user properly, a connect will fail.
I'm using MySQL_Workbench for this.
There is another issue with "root": Per Default it uses the auth-something plugin instead of "native-password"-something for authentification. You'd have to setup/correct that too, but only if you really want to use the "root"-account