There's a reasonable chance that this is down to a network level issue connecting to the database. Depending on whether you're running the application and database on the same box of course.
Try connecting to the database from the same machine using a different tool. You could set up a data source and test it from the control panel as an alternative. If the connection is slow from another tool test the connectivity between the servers for other types of connection (e.g. run a ping). It may be that it's resolving the server via broadcast rather than the domain, for instance. Or any number of other issues - firewall, switch, wins etc.
If you are connecting using integrated authentication also ensure that the database can resolve the application server as well as vice versa. This is part of the authentication process and I've seen it cause slow downs in creating database connections before.
In short, I'd be confident that this isn't a problem specific to delphi / sql, but something in the communications between your production servers.
Good luck!