It got worse. Once the modem was replaced, we couldn't get the WiFi system (Apple Time Capsule) to connect to the internet. The network was fine between the computers, and I could print to the wireless laser printer, but no internet. Also couldn't even make an ethernet cable connection, although the tech could get in with his laptop to link right up. I decided to reset the router part of the Time Capsule, but the procedure failed because of an ID conflict. Over a two hour call with a very good Charter Cable customer support, we tried a bunch of things to connect the Time Capsule, but after the third or forth try it--the TC--appeared to fail outright. It simply wouldn't reboot completely. Toast.
So we tried direct cable again, and the phone tech found it's a known compatibility problem between Macs and Charter--they fail to pick up the modem's ID automatically. The solution is to disconnect everything, have the office send a new ID, then make connections in the right order, and turn on the computer. On the third try of this, a connection was established. So we're back online, after a fashion.
We hooked the TC directly to the upstairs Mac by ethernet cable. It appeared, but would not accept a password to connect to it to get at its data. So the Time Machine backup data is in there, but I don't yet know how to get at it, and it's been a long day. I'm having SuperDuper run a full bootable backup of my main imaging computer--what the Time Capsule is supposed to be protecting--which will likely take an hour or two. Tina's computer is the one physically close to the modem, so it's the one that can go online now.
I'll see if the Apple Store has a "no charge if we can't fix it" policy for the TC as they do for computers, and if they don't, or if they can't fix it, I'll get a stand-alone router, preferably as powerful a one as possible, and use a hard connection instead of WiFi to run Time Machine on the imaging computer. This has been as long a day as returning from Ohio on Thursday.