Finally after months of mucking about, we are sharing an internet connection, halving the telephone cost.
The wireless card on my laptop gave up the ghost somewhere on my travels and I was never sure why. I bought a USB wireless card which appeared to work but didn't connect to Bee's new computer at all.
After an evening with a friend we decided my computer and the USB did connect to his network but it was slow and had no range.
So today I bought the fastest pc card and put it in. After 5 minutes fiddling we had a shared internet connection. So Bee has moved upstairs to her bedroom and we have lost the trailing wires over the floor. We can now ignore each other completely!
However all is not finished! We still can't share files or printers, but that can wait.