Comcast promised to send a service tech between 1 and 3. This is Service Visit #5. (Service Visits #s 3, 3a, 4 and 4a were either cancellations or no-shows, for assorted reasons.) Service Tech #3 turned up at 1 on the dot. According to him, he is a 14-year Comcast tech and has read the history of our service calls. This may perhaps explain his politeness. :)
In the end, he hooked up the second router, the one left by Service Tech #2, the one that Phone Tech Support Guy had told Roommate M was either not a router or was a very very old router, on account of service techs do not carry new routers in their trucks on service calls.
Apparently, it is indeed a router. It is a router provided by Comcast, meaning that Roommate M wasn't out of line in asking Comcast to provide service for it (although she probably yelled at them, which she ought not to have done).
Moreover, it is a functional and reasonably good router, although not the newest and most expensive model. The issue, apparently, is that Service Tech #2 did not set it up correctly, and left its settings in such a state that the troubleshooting which Roommate M did over the phone could not possibly have worked. Which it didn't.
Moreover moreover, Service Tech #3 says that, judging from the history of our service calls, Service Tech #2 was a contractor. This is important, because contractors are paid by the job. It is in fact to their advantage to hook up some piece of equipment--any equipment--and get out so they can move on to the next job. Service Tech #3 implied heavily, although of course did not state outright, that this is what happened with us and Service Tech #2 and the router.
Service Tech #3 tested both the modem and the router, all the cables, and ran various tests re: transmission speed, download speed, etc. Everything is working. I'm now writing to you from my laptop in my house on a working wireless system.
Service Tech #3 also spent an extra 10 minutes with Roommate M and her (desktop) computer, seeing whether there is any way M can get faster download speed. He finished up by giving us his tech number (we already had his name) and assuring us that we could call Comcast and request that he, specifically, be sent to us on future service calls--as long as we don't mind that we might need to wait a little longer for his exclusive assistance.
Finally, I should mention that Service Tech #3 didn't openly try to persuade us to spend more money on any Comcast product, although when M persisted in asking about faster download speed, he did finally allow as how money can be exchanged for goods and services re: Comcast's other internet service tiers.
To sum up: After receiving service from Comcast which varied from questionable to awful, we finally got a specific service tech who provided great service. Naturally, this only holds true if the wireless continues to work; M says that, after previous visits, the wireless worked while the service tech was in the house and stopped working when they left. We'll see how this one goes.