It is the drainage pipe not the downspout. So it is a repair for a plumber and digging it up is the only way to repair it?
Are you there?
I spoke with my plumber and he wasn't very helpful. Told me to stand out in rain and see if water comes out of the crack in the pipe (reasonable idea). Wanted to pull off my aluminum siding - there was no reason for that at all. You don't have to be a Master Plumber to see that the drainage pipe was nowhere near my siding.
The drainage pipe is cast iron. Would you replace with cast iron or PVC piping? Any idea how far down you would have to dig?