Then I plugged in the modem, which didn't power up. This turned out to be a dirty power connector, and a little jiggling fixed that up. But then the built-in fax software refused to recognise a modem hung off a USB port, expecting only the built-in modem (which I had omitted when I ordered the system, thinking that I have broadband and didn't need a modem).
So I downloaded some third party fax software that also hangs off the print driver. I installed and configured it, and configured the printing system to recognize it as a valid destination. It thought the modem was always busy. So I told it to use its "less strict" rules to determine modem availability. Then it would try to send, but the modem didn't see it. I realized I'd used the "null modem" cable adaptors, and swapped one end for the other pinout, implementing a straight through cable. Then it saw the modem, but it had never heard of a Hayes modem and wouldn't work.
Then I remembered the iMac had a built-in modem (as I had updated its modem firmware recently). So I fired up the iMac, moved the document, replugged the phone line in that room through the UPS/surge filter, and thence to the modem. It didn't work.
Then I remembered that outlet had been the old ISDN line, and didn't go anywhere any more. So I went down into the basement to repatch the phone wiring. It turns out I had already done so, all the jacks (except one that had mysteriously shorted a while back) were on the blue/white pair, the voice line. I had never doped out every set of wires to its jack, so I didn't know which one was the mud room (where the iMac currently lives). I put the toner on one set, and went upstairs to find it. Ah, that's the kitchen jack. I headed back down to the basement to try another one, and there was the cat, with a freshly killed mouse in her jaws.
After some touchy negotiating, I acquired the corpse from her and went outside to lay it to rest. As I was in my shirtsleeves and there's a foot of snow on the ground, I rather hurried. When I came back inside, I tried to brush/tap all the snow off my shoes, but I didn't get all of it. So when I went back into the (mud floored) basement, I coated my shoes with a generous ice-mud coating. I hooked up the toner to another set of wires and headed back up. So as not to track mud all over the floor, I kicked off my shoes at the top step. No joy on the downstairs outlets, so I tried the upstairs ones I could get to easily. This woke up my poor sick sweetie who wondered what was going on. I didn't want to burden her, so I just said I was debugging the phone wiring. No outlet seemed to be the right one, so back to the basement (putting my shoes back on) to try another circuit. Then back upstairs (taking my shoes back off) to see if I'd found the right outlet. Happily, this time I had. So I grabbed the butt set to try that circuit at the patch panel and went back downstairs (redon shoes). The butt set had dead batteries.
Back upstairs (take off shoes) and steal a phone from the dining room. Plug it into the wall jack in the mud room, and hey presto -- dial tone! Apparently the problem was either the patch cable to the UPS/filter or the filter itself. Go back downstairs (put on shoes), turn off work light, round up cat, come back upstairs, keep cat at bay while picking up shoes with one hand and putting the door back (sigh) and block it in place with a chair with the other hand. Time to wash off the shoes.
I didn't want to wash my dirty shoes in the sink with the dishes I eat off of (yes, I just ended a phrase with two prepositions), so I picked up a stack of dishes with my free hand to put aside. The dishes were full of water, which went everywhere.
I went ahead and washed off the shoes which were then wet, so I flung 'em into the mud room. Then I cleaned up the water everywhere and put the dishes back into the sink.
So I plugged the iMac's modem directly into the wall jack and tried to send from there. The built-in software didn't want to work with the built-in modem for some reason. So I copied the 3rd party software from the other machine and installed and configured it again. And that software seems capable of sending a fax.