Huzzah!!

I now have connectivity from the PC on my desk in the spare room to Toby's empeg sitting downstairs in the Lounge.

So what did it turn out to be?

One of the punch blocks had come adrift -- accounting for the lack of pin 1, and one of the patch cables was mangled -- accounting for the 3 common pins.

I got rid of the dodgy cable and repunched the blocks, and it seems to work fine now. I've not tried anything strenuous yet, though.

Hmm, sounds like you had a difficult case of.....
Multiple simultaneous faults!

Yes, folks even the most experienced troubleshooter can be
stopped in their tracks by this sort of occurrance. It tends to strike when you least expect it.
Be aware though that there is no easy & simple cure but a slow and methodical approach and a open mind will eventually result the faults being eliminated one at a time.