First step: removing the old drainpipe. We broke one of the old sections of terra cotta pipe with the brick hammer and got it out of the way. In that section, we found a tennis ball and a larger sponge rubber ball in the drainpipe--that can't have been helping flow. Then Les worked on trying to clear some of the other drainpipes on the house, while I worked on trying to lift out the other sections of pipe. I found it was most useful to insert the handle of the pickaxe as far as I could into the pipe and use that as a lever to pry the pipe out.
I worked my way up pretty quickly to the curve at the back of the house. There I discovered that what I thought was a curve in the pipe was actually a Y-joint. There was still a hole the size of my hand in the joint, so it was unambiguous that it had to be replaced.
But first it was necessary to dig out the lower pipe and get an end that was even enough to fit a connector on. This turned out to be more arduous than it might otherwise have been. The earth around it wsa very clayey, and it was moist from the previous day's rain. And the drainpipe turned out to be cracked, and our attempts to break it off evenly kept exposing more cracks. So we kept having to unearth more of the pipe and try again.
Eventually, Les went home to get a grinder to help with that trimming, and I went off to the hardware store to get the parts that we would need.
We failed several times with the grinder, but eventually got it trimmed even enough to get the FernCo connector on. By this time, though, Les had to leave. I continued digging the pipe out and digging out all the loose soil that we had gotten into the trench. It felt arduous to do so, but it didn't take that long. At 2:50, I set myself a time limit of 3:30 by which I would wimp out, but I finished by 3:10.
On Monday night, Les came over again, and we put in the new PVC drainpipe. This actually went fairly easily; it was just a matter of cutting the pipe to length, cementing it together, and sticking it in. The flexible rubber connectors made things much more tolerant. I wasn't nearly as sweaty after this part of the task.
One discovery during that evening: there's a heating vent in the crawl space underneath the house. The purpose of this is probably to keep the pipes warm to avoid freezing the pipes, but it's certainly adding to our heating bill.
So, we have a new drainpipe. It remains to be seen how many of the problems this fixes. But all in all, the job was not too arduous, and probably saved a lot of money compared to the cost of a contractor. And I do feel proud about doing that work. I still might have some second thoughts about doing it again, though...