Hope this is not a double-post. I posted some 20 minutes ago, and
nothing appeared.

Steve, I did not ignore everything. I think I did try everything
suggested here EXCEPT water blasting from the bottom of the hill.

did not try that because I am afraid I might clog up something that
would screw up the 11 working downspouts.

So, I do appreciate everything everyone suggested. And I did take
apart, waterblast from the top, etc as suggested, except for the one
part suggested.

Again, if I have to trench, I'd rather do that than risk screwing up
the rest of the system.