My down spout drain (the part under the concrete driveway) is plugged. How do I get it open?

You'll probably be best served by renting a long 'plumbing snake'. That's a long cable-tool that is used to clean out drain-lines when they become clogged a distance from it's opening. Run the tool into either end of the down spout and use it to remove the clog. It's easy to use once you have it in place, self-explanatory.