In general if you are having problems making a connection more than one environment it would indicate an issue with the connection details for the server itself. When you attempt to connect with a GUI tool other than in Dreamweaver what is the specific error message you get?
Is the connection a local one or to your hosted db? It is very common for host to restrict access to the db remotely. If this is the case I think you best bet would be to have a local MySQL server running. Please post back with what you discover and we will gladly help to guide you in the rite direction.