Better for the environment if you disconnect from the storm drain system altogether. Here in Portland OR they actually will pay you to disconnect your gutters from the storm drains and redirect the drainage onto your lawn and flowerbeds. Sure makes this kind of problem a thing of the past.

Here is a link that might be useful: portland's program

The downspout sections should be fastened together with screws or rivets. find the joint where the sections come together and remove the fastener and seperate. clean it out with a garden hose. If it is on piece from the gutter to the ground go up to the roof and try a grden hose there with a sprayer. It might break it loose. Otherwise try a plumbers snake. Also I would pull them out of the underground tile first so the crap goes out on the ground.