How can I remove a large obstruction from a storm drain pipe?
Depending on the location you could install a 4 inch or suitable size floor grate to prevent large items from entering the pipe. You could also fabricate something out of coarse screen, which in some locales is called "hardware cloth". Removing any obstructions will depend on whether you have access to only the entrance or also the exit. If you are clearing normal silt, sand, etc a power drain snake should work. If you are clearing a solid obstruction like a ball, you could try a large shop vac with a long length of hose attached. Swimming pool hose is fairly rigid, is flexible, comes in long lengths and more reasonably priced than regular vacuum hose. If both ends are exposed you could try blowing the ball out with a leaf blower from the exit end.