Have you located the terminal outlet of the pipe? It's most likely the clog will be at the outlet end.

I suspect the terminal outlet is under the front sidewalk. There's a storm sewer that runs perpendicular to the front sidewalk. Do you suppose there's any chance the pipe runs into the storm sewer, or is that illegal?

It's very unlikely that anyone would place an outlet below a walk. You might submit a picture or two in order to give the flavor of the area. One configuration I've seen before is a below-grade pipe whose outlet is at grade. The water must rise -- pushed up by flowing water behind it -- in order to get back to grade and escape. (Water remains in the pipe when the flow stops.) It's guaranteed that such a system will clog. On top of that, grass will grow over the drainage outlet and conceal it completely. Is it possible you could have anything like that?

Wow! I didn't realize that people would install a configuration like that. It makes no sense to me. I'll take a couple of photos and post them.

If you have a $100 or so, you can get a sewer company out to run a scope of the line. They come out with a camera and you can follow where it goes and see what happens to it.

Thanks, tanowicki.

Yardvaark, I'm posting a couple of photos to provide some context.

The photos help. They lead me to believe that the configuration I described above is a likely possibility. Can you tell by looking into the opening at base of downspout the general direction the underground pipe runs? You'll need to trace the pipe in order to find where it lets out. IF the installer used rigid PVC for all of the pipe (as opposed to black corrugated, which is soft) you could use a sharpened steel rod (about 5/16" to 3/8" dia.) to probe into the ground, feeling for the pipe. This way, you don't need to excavate the yard in order to "find" it. Keep probing, following it's path until you can't go anymore. Then dig to find it's end and discover it's condition. If the installer connected the PVC to black corrugated pipe, the probe probably won't work because the pipe wall is too soft and will be punctured, meaning that you won't feel where it is. In this case, follow the pipe by digging exploration holes through the sod until you find it. (Which is why you want to know the direction it takes off toward in the beginning.) Each time you expose the pipe, it's direction of travel will lead you to an educated guess about where the next hole should be dug. Since your yard is not large, two or three small holes should allow you to trace the pipe to its end, where you will dig, again, to discover its condition.

If the condition of the outlet is as speculated above -- buried, clogged and sod grown over -- then it's a matter of cleaning it out and maintaining it as such on a regular basis ... or reconfiguring the the drainage scheme so that it is above grade and would need little or no maintenance.

In all of this, I presume that the grade runs downhill toward the street. The picture doesn't actually guaranty that this is true. I'm speculating based on probability.

Yes, the grade runs slightly downhill toward the street. I have a pretty good idea where the line is likely to be. If it isn't where I think it is, I'll probably dig a trench perpendicular to the probable direction of the line until I run into it. Then I can dig the exploration holes you suggested to determine where the line ends. Thanks so much for your help, Yardvaark!